Magnetyzm: ilości, jednostki i relacje Jeśli od czasu do czasu potrzebujesz zaprojektować komponent ran, ale nie zajmujesz się nauką o polach magnetycznych na co dzień, możesz stać się zdezorientowanym co do wielu terminów użytych w arkuszu danych dla rdzenia reprezentują, w jaki sposób są ze sobą spokrewnieni i jak można ich użyć do wytworzenia praktycznego induktora. O twojej przeglądarce: jeśli te czasy postaci nie wyglądają jak znak mnożenia, lub widzisz wiele znaków zapytania lub symboli, takich jak lub sekwencji takich jak ampcannot, to proszę przyjąć moje przeprosiny. Indeks do jednostek wzmacniaczy magnetycznych w SI Ten zestaw stron internetowych wykorzystuje system jednostek znany jako SI (Systegraveme International). Aby uzyskać więcej informacji na temat SI i jak porównać to z innymi systemami, zobacz Systemy jednostek w elektromagnetyzmie. Ilości magnetyczne w SI Efektywna powierzchnia rdzenia reprezentuje pole przekroju jednej z jego kończyn. Zwykle odpowiada to ściśle fizycznym wymiarom rdzenia, ale ponieważ strumień może nie być rozłożony równomiernie, producent określi wartość Ae, która to odzwierciedla. Potrzeba obszaru rdzenia powstaje, gdy chcemy powiązać gęstość strumienia w rdzeniu (ograniczonym przez rodzaj materiału) z całkowitym strumieniem, który przenosi - w przykładowym toroidzie obszar ten można określić w przybliżeniu jako iloczyn wysokości rdzenia i różnica pomiędzy promieniem głównym i małym - A e 6,3 razy ((12,7 - 6,3) 2) 20,2 mm 2 Jednakże, ponieważ strumień koncentruje się tam, gdzie długość ścieżki jest krótsza, lepiej zastosować wartość podaną przez producenta - 19,4 mm 2. Dla prostego toroidalnego kształtu A e jest obliczany (Snelling), ponieważ Zakłada on, że kwadratowe krawędzie toroidalne są często zaokrąglone. Istnieje niewielka zmiana w kwestii obszaru: wartość producenta dla A e daje prawidłowe wyniki, gdy jest używana do obliczenia reluktancji rdzenia, ale może nie być idealna do obliczenia strumienia nasycenia (który zależy od najwęższej części rdzeń lub A min). W dobrze zaprojektowanym rdzeniu A min nie będzie bardzo różnił się od A e. ale miej to na uwadze. Efektywny obszar jest zwykle podawany w milimetrach kwadratowych. Wiele formuł w książkach danych domyślnie zakłada, że należy użyć wartości liczbowej w mm 2. Inne książki i te notatki zakładają mierniki do kwadratu. Efektywna długość efektywnej długości w SI Efektywna długość rdzenia jest miarą odległości, którą wędrują linie strumienia, tworząc jej pełny obwód. Zwykle jest to ściśle związane z fizycznymi wymiarami rdzenia, ale ponieważ strumień ma tendencję do koncentrowania się na wewnętrznych narożnikach ścieżki, producent określi wartość dla l, która to odzwierciedla. W przykładzie toroidalnym długość drogi może być określona w przybliżeniu jako czasy pędu (12,7,3) 2 29,8 mm Ponieważ jednak strumień koncentruje się tam, gdzie długość ścieżki jest krótsza, lepiej jest użyć wartości podanej przez producenta - 27,6 mm. Dla prostego kształtu toroidalnego l e jest obliczany jako Inny typ rdzeniowy, EE, pokazano na rysunku: EEE. Czerwona linia reprezentuje najkrótszą ścieżkę, jaką może obrać linia strumienia, aby okrążyć jądro. Zielona linia jest najdłuższa. Kolor niebieski to ścieżka o długości krótszej ścieżki plus cztery sektory, których promień wystarcza do pokonania drogi w połowie kończyn. Wszystko to jest trochę przybliżone, ale pamiętaj, że ponieważ tolerancje produkcyjne dotyczące przepuszczalności są często 25, nie ma sensu być dokładniejszym. Efektywna długość jest zwykle podawana w milimetrach. Wiele formuł w książkach danych domyślnie zakłada, że należy użyć wartości liczbowej w mm. Inne książki i te notatki zakładają mierniki. uarr Do początku strony Siła magnetomotoryczna Siła magnetomotoryczna w SI F m 0,25 razy 2 0,5 ampera Nie mieszaj siły magnetycznej z siłą pola magnetycznego (siła magnesowania). Analogicznie myślimy o płytach kondensatora z określoną siłą elektromotoryczną (EMF) pomiędzy nimi. Wysokość siły pola elektrycznego zależy od odległości między płytami. Podobnie, natężenie pola magnetycznego w rdzeniu transformatora zależy nie tylko od MMF, ale także od odległości, jaką musi pokonać strumień. Pole magnetyczne reprezentuje energię zmagazynowaną, a W jest energią w dżulach. Możesz także powiązać MMF z całkowitym strumieniem przechodzącym przez część obwodu magnetycznego, którego niechęć znasz. Jest tu wyraźna analogia z obwodem elektrycznym i Prawą Ohma, V I razy R. Analogia z potencjałem elektrycznym (napięcie) prowadzi do alternatywnej nazwy potencjału magnetycznego. Istnieje jednak ryzyko pomylenia z potencjałem wektora magnetycznego - który ma zupełnie inne jednostki. Specyficzny MMF jest wymagany do utrzymania zadanej wytrzymałości pola wzdłuż znanej długości ścieżki - Praktyczne uzwojenia cewki są wykonane z drutu miedzianego, który ma zdolność przenoszenia prądu ograniczoną głównie przez jego przekrój. W związku z tym istnieje ograniczenie do MMF cewki w ciągłej pracy wynoszącej około 3,5 x 106 obrotów na metr kwadratowy otworu. Wytrzymałość pola magnetycznego Wytrzymałość pola magnetycznego w polu SI natężenie pola magnetycznego alias natężenie pola magnetycznego alias pola pomocniczego alias Pseudolokość pola magnetycznego Siła magnetyczna Kiedy przepływ prądu zawsze towarzyszy mu pole magnetyczne. Naukowcy mówią o tym, że jest to spowodowane poruszającymi się ładunkami elektrycznymi - rozsądny opis elektronów płynących wzdłuż drutu. Siła lub natężenie tego pola otaczającego prosty drut jest określone przez to, w którym r, odległość od drutu jest mała w porównaniu z długością drutu. Sytuację dla krótkich przewodów opisuje równanie Biota-Savarta. Przy okazji, nie mylić prędkości ładunków (takich jak elektrony) z prędkością sygnału podróżującego w dół drutu, w którym się znajdują. Pomyśl o tym, że sygnał jest granicą między elektronami, które zaczęły się poruszać, a tymi, które mają jeszcze iść. Granica może zbliżać się do prędkości światła (3x10 8 m s -1), podczas gdy same elektrony dryfują (średnio) około 0,1 mm s -1. Elektrony zostałyby wyprzedane przez ślimaka - nawet gdyby nie było pośpiechu. Możesz sprzeciwić się, że pola magnetyczne są również wytwarzane przez magnesy trwałe (takie jak igły kompasu, zaczepy drzwiowe i uchwyty do przechowywania lodówek), w których przepływ prądu nie jest oczywisty. Okazuje się, że nawet tutaj elektrony poruszają się na orbitach wokół jąder lub wirują na własnej osi, odpowiedzialne za pole magnetyczne. Dualność ze światem elektrycznym W tym przykładzie natężenie pola wynosi - H 0,5 27,6 x 10 -3 18,1 A m -1 Analogia do natężenia pola elektrycznego jest matematyczna, a nie fizyczna. Pole elektryczne ma jasno określone znaczenie fizyczne: po prostu siła wywierana na ładunek testowy podzielona przez ilość ładunku. Natężenia pola magnetycznego nie można zmierzyć w ten sam sposób, ponieważ nie ma magnetycznego monopolu równoważnego ładunkowi testowemu. Nie należy mylić natężenia pola magnetycznego z gęstością strumienia. B. Jest to ściśle związane z natężeniem pola, ale zależy również od materiału w polu. Ścisła definicja H to ta formuła ma zastosowanie ogólnie, nawet jeśli materiały w polu mają niejednolitą przepuszczalność lub stały moment magnetyczny. Jest rzadko stosowany w konstrukcji cewek, ponieważ zwykle można uprościć obliczenia, zakładając, że w polu przepuszczalność można uznać za jednorodną. Przy takim założeniu mówimy zamiast tego, że strumień wyłania się również z magnesu trwałego, nawet gdy nie ma żadnych drutów do narzucenia pola. Natężenie pola około 2000 A m-1 jest mniej więcej granicą dla rdzeni wykonanych z proszku żelaza. W idealnym cewce strumień generowany przez jeden z jego zwojów otaczałby wszystkie pozostałe zwoje. Rzeczywiste cewki zbliżają się do tego ideału, gdy wymiary przekroju poprzecznego uzwojenia są małe w porównaniu z jego średnicą, lub jeśli rdzeń o wysokiej przepuszczalności prowadzi strumień prosto dookoła. W przypadku dłuższych cewek powietrznych sytuacja prawdopodobnie będzie bliższa temu pokazanemu na rys. TFK: widzimy tutaj, że gęstość strumienia maleje w kierunku końców cewki, ponieważ niektóre strumienie przyjmują krótkie cięcie omijając zewnętrzne zwoje. Załóżmy, że prąd w cewce wynosi 5 amperów, a każda linia strumienia reprezentuje 7 mWb. Centralny trzy z kolei łączy wszystkie cztery linie strumienia: 28 mWb. Dwa zewnętrzne zwoje łączą tylko dwie linie strumienia: 14 mWb. Możemy obliczyć całkowite wiązanie strumienia dla cewki jako: lambda 3times28 2x14 112 mWb-t Przydatność tego wyniku jest taka, że pozwala nam obliczyć całkowitą indukcyjność własną cewki, L: L lambda I 1125 22,4 mH Ogólnie, tam, gdzie zakłada się idealną cewkę, widzisz wyrażenia z udziałem N razyPhi lub N razydPhidt. Dla większej dokładności zamieniasz lambda lub dlambdadt. Możesz zostać wybaczony za myślenie, że nie byłoby potrzeby, aby przeliterować, czym jest prąd. To oczywiste, że Twoim błędem jest zapomnieć o tym, jak ciężko wszyscy autorzy elektromagnetyzmu starają się zaciemnić już trudny temat. Oto problem. Rysunek TMX pokazuje dwie cewki o różnej liczbie zwojów, ale o tej samej sile magneto-motorycznej. Rozważając MMF, nie ma znaczenia, czy masz dwanaście zwojów drutu z jednym wzmacniaczem, czy trzy obroty z czterema wzmacniaczami lub dwoma zwojami z sześcioma wzmacniaczami. Jeśli chodzi o MMF, to wszystko ma zaledwie dwanaście amperokrętów. Otrzymasz tylko to samo pole magnetyczne w każdym przypadku. Rozumowanie tego szczegółu dotyczącego liczby zwojów i liczby wzmacniaczy nie ma znaczenia, a jedynie iloczyn tych dwóch. niektórzy pisarze decydują się powiedzieć, że prąd ma dwanaście amperów. Piszą I 12 A i pozostawiają ci decyzję, który scenariusz doprowadził do tego prądu. Ta podstępna praktyka przenosi się również na formuły. Co jest w porządku, o ile jest spójne i jasne dla czytelnika, co się dzieje. Jeśli prąd zmienia się wtedy, zgodnie z Ustawą Faradays mamy indukowane napięcie. Następnie należy pamiętać, że indukowane napięcie to jeden obrót, a nie całkowite napięcie cewki. Dwuznaczność zaczyna wkradać się. To zależy, czy jesteś bardziej zainteresowany fizyką lub inżynierią. Te strony mają ten drugi widok i odróżniają bieżący od MMF. Obecne tutaj jest to, co zwykły amperomierz odczytuje, a liczba zwojów cewki. N, jest napisane wprost. Fizycy podążają w końcu, ponieważ, chociaż można mówić o niechęci jako amperokrętwach na Webera, indukcyjność jako zakręt weselny na ampera jest nieco wymyślna - nawet jeśli raczej dość dobrze oddaje koncepcję sprzężenia strumienia. Ale przepuszczalność jako skręty weselne na amperometr. Strony te są przekształcane na duże litery I zarówno dla prądu stałego, jak i dla prądu podanego jako wielkość RMS, podczas gdy małe i oznaczają wartości chwilowe prądu zmieniającego się w czasie. Ciekawostka: dlaczego symbol używany do prądu rzekomo oznacza intensywność elektryczną, w przeciwieństwie do całkowitej ilości energii elektrycznej (ładunek). Maxwell. jednak używał symbolu C dla prądu i używanej intensywności elektrycznej, aby odnieść się do pola elektrycznego: co większość ludzi dzisiaj zna jako siłę pola elektrycznego. Tak to idzie. Gęstość prądu Strumień zmieniający czas wytwarza indukowane napięcie (EMF) - Jeśli możesz wykonać tę pięciostopniową sekwencję, wówczas budowanie mentalnego obrazu komponentu magnetycznego staje się prostsze. Pamiętaj, że wkładasz prąd i odzyskujesz indukowane napięcie. W rzeczywistości, jeśli można traktować przepuszczalność jako liniową, wówczas stałe N. l e. mu i A e można połączyć w jedną stałą dla uzwojenia, która nazywa się (niespodzianką) indukcyjnością. L - Podaję jednostki bazowe dla wszystkich wielkości w tym równaniu, umożliwiając osobom poszukującym dreszczyku emocji wykonanie analizy wymiarowej weryfikującej, czy jest ona spójna. Racja, więc nasza pięciostopniowa relacja między prądem a EMF sprowadza się do: Być może masz zamiar narzekać, że znasz EMF na swoim uzwojeniu, ale nie znasz prądu w nim. Odpowiedź brzmi, że proces działa wtedy odwrotnie - prąd narasta, aż indukowane napięcie wystarcza, aby przeciwstawić się przyłożonemu napięciu. Możesz dowiedzieć się więcej, patrząc na prawo Faradays. Jak wziąć pod uwagę obecność uzwojeń wtórnych w transformatorze Jednym ze sposobów jest wykonanie pierwszych czterech kroków powyższej sekwencji i zastosowanie ich oddzielnie do każdego uzwojenia (pierwotnego lub wtórnego). Suma arytmetyczna na wszystkich uzwojeniach daje całkowity strumień rdzenia. Od czasu zmiany strumienia masz indukowane napięcie w każdym uzwojeniu (ponieważ znasz także liczbę zwojów dla każdego z nich). Istnieją mniej żmudne metody analizy pracy transformatora, z którymi prawdopodobnie lepiej byłoby skorzystać. Ale to już inna historia. W relacji pomiędzy termodynamiczną i konfiguracyjną entropią. Geneza drugiej zasady termodynamiki. Ta strona jest częścią zestawu stron, które należą do przecięcia zainteresowań autora w fizyce i matematyce. Uwaga: niebieskie łącza są wewnętrzne, zielone łącza to linki zewnętrzne kursywą otwartą w nowym oknie. Pytanie Istnieją dwie wersje entropii znane w nauce. Jedna to standardowa, tradycyjna, termodynamiczna entropia. zwykle jest to omawiane w kontekście, na przykład, umieszczenia gorącego kamienia w kuble chłodnej wody: po chwili kamień ochładza się i woda ogrzewa się, obie uzyskują tę samą temperaturę i osiągają równowagę termodynamiczną . (Patrz rysunek poniżej, po lewym kliknięciu przycisku, aby pozwolić mu działać.) Zakładamy, że nie ma napływu energii z zewnątrz do wiadra, ani żadnej utraty energii z wiadra do środowiska. Tak więc, kamień wiszący jest uważany za system zamknięty. () Druga to mniej znana, konfiguracyjna lub logiczna entropia. typowy kontekst, w którym jest omawiany, to umieszczenie gazu zamkniętego w pojemniku w środku pomieszczenia, w którym znajduje się inny gaz o tym samym ciśnieniu, a następnie pokrywka pojemnika zostaje otwarta, a jego gaz zostaje uwolniony. Cząsteczki gazu znajdujące się w pojemniku rozpraszają się i mieszają z cząsteczkami gazu w pomieszczeniu, a po chwili oba gazy tworzą jednorodną mieszaninę. (Rysunek poniżej, po prawej stronie, symulując tylko cząsteczki gazu w pojemniku, kliknij przycisk, aby pozwolić mu działać.) Ponownie, uważamy, że pokój jest odizolowany od wpływów zewnętrznych, więc jest to również system zamknięty. Twierdzenie w przypadku entropii konfiguracyjnej jest takie, że początkowo w układzie jest więcej porządku, ponieważ cząsteczki tych dwóch gazów zostały rozdzielone, ale wraz z upływem czasu, a cząsteczki mieszają się, kolejność maleje, a tym samym wzrasta entropia konfiguracji. Pytanie brzmi: czy istnieje jakiś głębszy związek między dwoma rodzajami entropii, czy też ich podobieństwa są jedynie pozorne Czy istnieje jakieś podstawowe prawo, które powoduje dwie wersje, lub czy są one związane jedynie przez powierzchowną analogię? Gorący kamień jest umieszczony w wiadrze z zimną wodą po chwili oba osiągają równowagę termodynamiczną. Cząsteczki zaczynają od uporządkowanej struktury i rozpraszają się w dostępnej przestrzeni. The Contention Scientists nie zgadzają się co do tego, czy dwie wersje entropii są ze sobą powiązane. Wielu znanych autorów książek z dziedziny fizyki, skierowanych do szeroko wykształconej publiczności, milcząco zakłada, że te dwie koncepcje entropii rzeczywiście są ze sobą powiązane, tak że mówienie o jednym jest jak mówienie o drugim. Tacy autorzy nawet nie zawracają sobie głowy rozróżnianiem tych dwóch: mówią o uporządkowaniu i zaburzeniu (entropii konfiguracyjnej) w kontekście drugiej zasady termodynamiki (gdzie mowa o entropii termodynamicznej powinna być odpowiednia, jeśli dostrzegli różnicę między tymi dwoma elementami; ). Na przykład, według Stephena Hawkinga: Niewielkie zachowanie obszaru czarnej dziury bardzo przypomina zachowanie fizycznej wielkości zwanej entropią, która mierzy stopień zaburzeń systemu. Jest sprawą powszechnego doświadczenia, że zaburzenie będzie wzrastać, jeśli rzeczy zostaną pozostawione samym sobie. (Można tylko przestać robić naprawy wokół domu, aby to zobaczyć) Można stworzyć porządek z nieładu (na przykład można malować dom), ale to wymaga nakładu wysiłku lub energii, a więc zmniejsza ilość zamówionej energii dostępnej . Dokładne określenie tej idei jest znane jako druga zasada termodynamiki. Stwierdza, że entropia izolowanego systemu zawsze wzrasta, a gdy dwa systemy są ze sobą połączone, entropia połączonego układu jest większa niż suma entropijnych systemów. Rozważmy na przykład system cząsteczek gazu w pudełku. Cząsteczki mogą być uważane za małe kulki bilardowe, które nieustannie kolidują ze sobą i odbijają się od ścian pudła. Im wyższa temperatura gazu, tym szybciej przemieszczają się cząsteczki, a więc im częściej i trudniej zderzają się ze ścianami pudła i tym większy nacisk zewnętrzny wywiera na ściany. Załóżmy, że początkowo cząsteczki są ograniczone do lewej strony pudełka przez partycję. Jeśli partycja zostanie następnie usunięta, cząsteczki będą się rozprzestrzeniać i zajmą obie połówki pudełka. Po jakimś czasie mogą przypadkiem znaleźć się w prawej połowie lub w lewej połowie, ale jest bardziej prawdopodobne, że w obu połówkach będą mniej więcej równe liczby. Taki stan jest mniej uporządkowany lub bardziej nieuporządkowany niż stan pierwotny, w którym wszystkie cząsteczki były w połowie. Mówi się więc, że entropia gazu wzrosła. W krótkiej historii czasu 1 pkt. 106. Podobnie, według Briana Greene'a (podkreślenie w oryginale): Po pierwsze, entropia jest miarą ilości zaburzeń w systemie fizycznym. . Po drugie, w układach fizycznych z wieloma składnikami. istnieje naturalna ewolucja w kierunku większych zaburzeń, ponieważ nieporządek można osiągnąć na wiele innych sposobów niż porządek. W języku entropii jest to stwierdzenie, że systemy fizyczne ewoluują w kierunku stanów wyższych entropii. W The Fabric of the Cosmos, 2 str. 154. Tendencja systemów fizycznych do ewolucji w kierunku stanów o wyższej entropii jest znana jako druga zasada termodynamiki. ibid, 2 p. 156. Lub, rozważmy Paula Daviesa, innego znanego i popularnego autora: Tak zwana druga zasada termodynamiki jest często wyrażana przez powiedzenie, że każdy zamknięty system dąży do stanu całkowitego chaosu lub chaosu. . Jedna miara bezlitosnego wzrostu chaosu używa pewnej ilości, zwanej entropią, która jest określona jako z grubsza mówiąc, stopień nieporządku w systemie. Drugie prawo stwierdza następnie, że w zamkniętym systemie całkowita entropia nigdy nie może w najlepszym wypadku spaść, pozostaje taka sama. Prawie wszystkie naturalne zmiany mają tendencję do zwiększania entropii i widzimy, że drugie prawo działa w naszym otoczeniu. Jednym z najbardziej rzucających się w oczy przykładów jest to, że słońce powoli spala swoje paliwo jądrowe, wyrzucając ciepło i światło bezpowrotnie do głębin kosmosu i podnosząc entropię kosmosu z każdym uwolnionym fotonem. W końcu słońce skończy się z paliwa i przestanie świecić. Ta sama powolna degeneracja dotyka wszystkie gwiazdy we wszechświecie. W połowie XIX wieku ten ponury los stał się znany jako kosmiczna śmierć ciepła. In About Time, 3 p. 34. Jak widzimy, znani autorzy i naukowcy nie przebierają w słowach, jeśli chodzi o identyfikację wzrostu entropii wraz ze wzrostem zaburzeń. Zauważ, jak Davies w ostatnim fragmencie przechodzi w tym samym tchnieniu od wersji konfiguracyjnej, która widzi entropię jako zaburzenie w wersji termodynamicznej, która widzi entropię jako śmierć cieplną (zasadniczo jako utratę zdolności do produkowania użytecznej pracy). Jednak niektórzy inni, mało znani autorzy wolą widzieć niemożliwą do pokonania lukę między termodynamiczną i konfiguracyjną entropią. Mówi się, że drugie prawo dotyczy termo dynamiki, a termo oznacza ciepło, nie zapominajcie, że ludzie uważają, że obserwacja, że zarówno entropia konfiguracyjna, jak i termodynamiczna mają tendencję do wzrastania, jest dziwnym zbiegiem okoliczności, zwykłą analogią, i że nie powinniśmy za bardzo czytać w tym analogia. Wskazują, że entropia termodynamiczna jest mierzona w określonych jednostkach, mianowicie dżulach na stopniach Kelvina, podczas gdy konfiguracyjna jest tylko liczbą, bez żadnych jednostek. (Entropia konfiguracyjna jest logarytmem wszystkich możliwych układów, np. Cząsteczek, które skutkują nierozróżnialnymi konfiguracjami, a zatem jest czystą liczbą). Następnie zauważają, że wzrost entropii termodynamicznej zmniejsza naszą zdolność do wykonywania użytecznej pracy (np. Do zasilania maszyny). ), ale nie ma takiego pojęcia w przypadku entropii konfiguracyjnej. Najbardziej głośnym z tych naukowców jest Frank L. Lambert, emerytowany emerytowany profesor chemii w Occidental College w Los Angeles w Kalifornii, który dosłownie wypełnił każdy zakątek i każdą szczelinę, która dotyczy 2. zasady termodynamiki w sieci, zwalczając pomysł, że entropia termodynamiczna i konfiguracyjna są ze sobą powiązane. Zgodnie z tym artykułem z Wikipedii znany jest on ze swojego poparcia dla zmiany definicji entropii termodynamicznej jako zaburzenia w tekstach ogólnej chemii w USA i zastąpienia jej przez oglądanie entropii jako miary rozprzestrzeniania energii. Poniższy fragment artykułu z Wikipedii na temat drugiej zasady termodynamiki wygląda tak, jakby pochodził bezpośrednio z własnych stron profesora Lambertsa. Pojęcie entropii w termodynamice nie jest identyczne z powszechnym pojęciem nieporządku. Na przykład, termodynamicznie zamknięty układ pewnych roztworów ostatecznie przekształci się z mętnej cieczy w klarowny roztwór zawierający duże uporządkowane kryształy. Większość ludzi określiłaby ten stan jako bardziej nieuporządkowany niż ten drugi. Jednak w sensie czysto termodynamicznym entropia zwiększyła się w tym układzie, a nie zmniejszyła się. Jednostkami miary entropii w termodynamice są jednostki energii na jednostkę temperatury. To, czy człowiek postrzega jeden stan systemu jako bardziej uporządkowany niż inny, nie ma wpływu na obliczenie tej ilości. Powszechne przekonanie, że entropia w termodynamice jest odpowiednikiem popularnej koncepcji zaburzenia spowodowało, że wielu nie-fizyków całkowicie błędnie zinterpretowało to, o co naprawdę chodzi w drugiej zasadzie termodynamiki. Cóż, jeśli profesor Lambert ma rację, oprócz nie-fizyków wygląda na to, że kilku prawdziwych fizyków (w tym tacy luminarze, jak Stephen Hawking, Brian Greene i Paul Davies) również całkowicie błędnie interpretuje, co jest drugą zasadą termodynamiki tak naprawdę, podczas gdy prof. Lambert (chemik) rozumiał głębiej entropię i drugie prawo. Czy to prawda? Ale profesor Lambert jest daleki od samotności w odrzuceniu związku między termodynamiczną i konfiguracyjną entropią. Jest wielu innych naukowców, którzy zgadzają się z nim, ponieważ jego udana kampania oczyszczenia amerykańskich podręczników chemii z skazy tego zamieszania pokazuje. Jeszcze inni wyciągają całkiem różne wnioski wychodząc z założenia, że entrodyka termodynamiczna i konfiguracyjna nie są ze sobą powiązane. Na przykład Brig Klyce, na tej stronie. argumentuje, że Ziemia nie jest termodynamicznie zamkniętym systemem, ponieważ otrzymuje napływ energii od Słońca, ale twierdzi, że musi to być system zamknięty (tzn. w odniesieniu do porządku), ponieważ termodynamika i entropia konfiguracyjna (lub: energia i porządek) nie są ze sobą powiązane: napływ energii nie może spowodować zwiększenia porządku. Tak więc Klyce próbuje wyjaśnić wzrost porządku biologicznego na Ziemi i twierdzi, że musi mieć jakieś pochodzenie inne niż energia otrzymana od Słońca. Używa tego argumentu do poparcia pojęcia panspermii, hipotezy, że życie nie ewoluuje na Ziemi, ale zostało tu wstrzyknięte z kosmosu (teoria, która pozostawia bez odpowiedzi pytanie, gdzie i jak życie pojawiło się pierwsze, ale to jest inny problem) . Stwierdza, że życie otrzymało takie zastrzyki porządku spoza Ziemi i dlatego wydaje się wysoce uporządkowane. Jego pogląd, oczywiście, może być również wykorzystany do poparcia kreacjonistycznego poglądu, że życie nie ewoluowało za pomocą doboru naturalnego, ale zostało stworzone na Ziemi przez jakiegoś Inteligentnego Projektanta. (Klyce przyznał mi się tak bardzo, w osobistej komunikacji). Widzimy więc, że spór o powiązanie między termodynamiczną i konfiguracyjną entropią ma konsekwencje wykraczające poza fizykę. Rezolucja Poniżej pokażę, że dwie wersje entropii są konsekwencją głębszego matematycznego wyniku faktycznie statystycznego, gdzie głębiej nie musi oznaczać trudniej zrozumieć, że jest on dość prosty do uchwycenia. Więc Hawking - et-al. pogląd będzie uzasadniony, podczas gdy próba przepisania amerykańskich podręczników chemii okaże się bezsensowna. Zanim jednak sformułuję twierdzenie matematyczne i udowodnię je, wolę odpowiednio zmotywować czytelnika do obserwacji. Przyjrzyjmy się jeszcze raz figurze przedstawiającej cząsteczki rozpraszające się w przestrzeni (jeszcze raz, naciśnij): Co tu mamy? Są to prawdziwe molekuły, które rozpraszają się w przestrzeni. Oczywiście, że nie. To tylko niektóre symulowane cząsteczki, zwykłe koła pomalowane na fioletowo, które poruszają się po programie uruchamianym po załadowaniu tej strony internetowej i naciśnięciu przycisku. W rzeczywistości poczekaj chwilę: te kręgi nie są nawet przenoszone. Pomyśl o tym, nic się tu nie porusza. Ekran komputera zawiera kilka pikseli, a program czasami maluje niektóre z nich na fioletowo, innym razem na to samo białe piksele i tak dalej. Piksele nie poruszają się po ekranie, są po prostu w stałych lokalizacjach. Program nakłania Cię do przekonania, że kręgi poruszają się, malując piksele w różnych kolorach, we właściwym czasie. Ale przysięgam, że nie zrobiłem nic w tym programie z wyraźnym celem, aby cię nakłonić do przekonania się, że istnieją kręgi, które rozpraszają Wszystko, co zrobiłem, to, że poprosiłem program, aby narysował fioletowe kółko wokół każdego punktu, najpierw układając punkty w uporządkowany moda (100 punktów w matrycy 10 x 10), a następnie przesuń każdy punkt osobno, niezależnie od tego, gdzie są inne punkty, do sąsiedniej lokalizacji. (Sąsiednie oznacza położenie w ustalonej odległości od podanej, pod kątem losowym, dlatego nowa lokalizacja znajduje się w dowolnym miejscu na obwodzie koła ześrodkowanym w poprzednim miejscu iz promieniem danej ustalonej odległości). Nie wydałem żadnego wyraźnego polecenia aby się rozproszyć, nie było dla nich żadnego porządku, aby oderwać się od środka figury. A jednak robią tak, jak prawdziwe cząsteczki gazu w prawdziwym pomieszczeniu. Dlaczego to jest połączenie Dobra, cząsteczki są rzeczami fizycznymi, przenoszą swoją masę w rzeczywistej przestrzeni i moglibyśmy spróbować zbadać, dlaczego rozpraszają się, stosując znane prawa fizyki. Ale te punkty Dlaczego, na ziemi, również się rozpraszają. Nie mamy tu żadnej fizyki, wszystko dzieje się w wirtualnej przestrzeni, w komputerze. Oczywiście można twierdzić, że istnieje coś fizycznego, które implementuje te punkty i maluje je jako purpurowe kręgi: jego bity w układach pamięci komputera. Jasne, ale związek między punktami i bitami w chipach komputerowych jest tak eteryczny, że nie można ustalić, które bity wykonują. W rezultacie bity nie rozpraszają się w układach komputerowych. Co więcej, twój komputer i jego sprzęt są całkowicie nieistotne, ponieważ program ten może być uruchamiany na maszynie Turinga, abstrakcyjnie, matematycznie, jak zapewni to każdy student pierwszego roku informatyki. Dzieje się tu coś innego, co nie ma nic wspólnego z fizyką: w kosmosie nie ma ani prawdziwych molekuł, ani też kamieni chłodzących. Mamy trzeci przykład rozpraszania powyżej, trzeci rodzaj entropii, niezależny od dwóch pozostałych fizycznych. Coś w rodzaju entropii i drugiej zasady termodynamiki można zaobserwować nawet abstrakcyjnie, matematycznie, bez jakiejkolwiek materialnej implementacji, bez fizycznej podstruktury, która uczyniłaby ją rzeczywistą. Hmm. Zbyt wiele entropii, nie sądzisz, że zbyt wielu jest po prostu analogią ze sobą, przez zwykły zbieg okoliczności. Powinniśmy stać się podejrzliwi z tak wieloma zbiegami okoliczności i szukać czegoś głębszego, co leży u podstaw i łączy je wszystkie. A ponieważ ten trzeci rodzaj entropii nie jest nawet fizyczny (czy możemy go nazwać entropią wirtualną), równie dobrze możemy zapomnieć na chwilę o fizyce i najpierw starać się wyjaśnić ten trzeci rodzaj, ponieważ wydaje się czystszy, bez żadnego materialnego bagażu pozostałych dwóch przypadkach. Po wyjaśnieniu, w jaki sposób dzieje się to wirtualne rozproszenie, możemy zobaczyć, w jaki sposób uzyskuje on fizyczne implementacje wyjaśniające termodynamiczne i konfiguracyjne przypadki entropii. Zobaczmy więc, co chcemy wyjaśnić, dlaczego dany punkt w przestrzeni (jedno z tych kół), które wykonuje przypadkowy spacer, oddala się średnio od danej pierwotnej lokalizacji. Ta ostatnia kwalifikacja jest bardzo ważna: musi to być średnia odległość od pierwotnej lokalizacji, ponieważ przypadkowy spacer oznacza, że punkt może wrócić do pierwotnej lokalizacji, z tego, co wiemy. Ale jeśli powtórzymy eksperyment dużo razy i wyskalujemy położenie punktu za każdym razem, powinniśmy stwierdzić, że punkt zwiększa jego odległość od pierwotnej lokalizacji. Ale dlaczego . Oto proste jakościowe wyjaśnienie: Powyższy rysunek przedstawia punkt oznaczony fioletową kropką na współrzędnych (x, y). Punkt ma rozpocząć swój losowy spacer w punkcie początkowym, oznaczony (0, 0), i teraz rozważa przeskok losowo w dowolnym miejscu na obwodzie czarnego koła, ponieważ tak to się porusza: w każdej chwili jest on niektóre lokalizacje (x, y), aw następnej jednostce czasu znajduje się gdzieś w odległości 1 jednostki odległości od (x, y), poruszając się pod kątem losowym. Oto kluczowe pytanie: mimo że wszystkie punkty na obwodzie czarnego koła mają równe prawdopodobieństwo otrzymania punktu (to jest dane), ile z nich oznacza, że punkt odejdzie od (0, 0) i jak wiele osób, które będą się do niego zbliżać Poniższa ilustracja odpowiada na to pytanie: Te punkty, które oznaczają, że punkt (x, y) przesuną się dalej od miejsca pochodzenia (0, 0) zostały zaznaczone na czerwono, a te, które sugerują, że (x, y) zostaną przesunięte bliżej pozycji (0, 0) w kolorze zielonym. Nie jest tak, że czerwone punkty są większe niż zielone (oba są nieskończone), ale długość czerwonego łuku jest dłuższa niż długość zielonego łuku, więc (x, y) ma większe prawdopodobieństwo zakończenia na czerwonym (od hotelu), a nie na zielonej (bliżej) części kolorowego koła. Powyższe jest jakościowym wytłumaczeniem, ale istnieje również ilościowe. Możemy obliczyć, jak szybko punkt (x, y) będzie się dystansował od początku (0, 0), zakładając powyższe reguły ruchu, pod warunkiem, że dokonamy formalności. However, if the reader feels uncomfortable with formulas and math, please note that there is nothing essential to be missed if the proof of the following theorem is skipped just make sure you read the theorem itself and understand its statement, because it is of central importance in this whole discussion. Definition. A 2D random walk is an infinite sequence of points p 0 . p 1 . on the 2-dimensional Euclidean plane such that each point p k has a distance of 1 from its previous point p k 1 . for all k gt 0. Point p 0 is called the origin of the walk, and point p k is called its k-th step . The definition implies that we dont care about the direction of the straight line defined by points p k and p k 1 . therefore the direction of this line is random hence the term random walk. Theorem (of dispersion in 2D space ). The expected distance between the origin p 0 and the n - th step p n of a 2D random walk is equal to . (Here, expected distance refers to the mean value of distances from the origin p 0 of the n - th steps of a large number of 2D random walks that share a common origin p 0 .) Proof: Think of the 2D plane as the plane of complex numbers, and place the origin p 0 at (0, 0). Let (x, y) be the coordinates of the n - th step p n in a 2D random walk. Therefore, as a complex number z, point p n would be written as z x i y. Recall that each complex number x i y can also be written using Eulers exponential notation as follows: where z is the modulus, or distance of z from the origin p 0 0 i 0, and u is the phase, or angle between the x - axis and the line that connects z with the origin p 0 . Now, if we fix the modulus z to the value 1 (since point z p n differs by this fixed distance from its previous point p n - 1 in the random walk) and allow the phase u to vary randomly in the interval 0, 2) (since the angle between successive points is arbitrary), then the new position z of (x, y) after n steps on the complex plane must be given by the following sum: Recall that the absolute square w 2 of a complex number w (i. e. the square of its distance from the origin) is equal to w w where w is the conjugate of w, i. e. w x i y w e - i u . So the absolute square of z in the above formula, which is equal to z z . is given by: Now, lets try to compute the mean value of the quantity z 2. We will use angle brackets (lt gt) to denote mean values. We have: Since both angles u j and u k are random variables with identical means, their difference ( u j u k ) is also a random variable with mean 0 (zero). This means that the whole formula of the mean value to the right of the plus sign, above, is 0 (zero). Thus, simplifying we get: Hence, taking the square root on both sides, we find that the root-mean-square distance z rms after n unit steps is: The root-mean-square is the average distance of z (or point p n ) from the origin p 0 . which is what we wanted to show. If n represents time in the above calculations, then the theorem tells us that at time n the point that performs a random walk is expected to be found at an average distance of from the origin (point of departure). This result is actually the same as found by Einstein in his famous papers of 1905 and 1906 on Brownian motion, 4 except that Einsteins calculations and notation are much harder to follow. The notation used in the above proof was taken from Weisstein, 1997 (p. 1524). 5 The above dispersion theorem tells us why the circles that perform random walks and are drawn by the program disperse on average, even though the program does not give them any explicit command to do so. The theorem explains what I earlier called virtual entropy. Now its not too difficult to see how the configurational and thermodynamic dispersals (and their associated notions of entropy) are simple physical implementations of the above mathematical result. The configurational case is trivial to see. We assumed molecules of a gas in a container covered with a lid, placed at the center of an isolated room that contains a different gas. Suppose the pressure in the two gases is identical. The molecules of the gas in the container (as well as those outside) perform approximations of random walks as they meet and bounce off one another. When we open the lid of the container the molecules of its gas keep performing random walks, but now they are permitted to meet and bounce off any kind of molecule: either of the same gas, or of the gas outside. So they disperse in space just as the purple circles in our simulation do, for the statistical reason described in the dispersion theorem, even though they dont move at a fixed distance every time, and even though they are not restricted to move on a 2-D plane. (What was proven by the theorem in two dimensions holds also in three dimensions, except that the average speed of dispersal in not equal to but slower. The proof is considerably more complex, thats why it was given in two dimensions and with a fixed distance of movement.) People often become confused with variations in the physical details of this experiment. They consider the room empty of matter (a vacuum), so when the lid is opened the molecules of the gas in the container swoosh out and quickly spread throughout the room without performing random walks. W porządku. The molecules of a gas under normal temperature move at dizzying speeds all the time anyway. (According to this article by Prof. Lambert, At the usual lab temperature, most water molecules are moving around 1000 miles an hour, with some at 0 and a few at 4000 mph at any given instant.) We are not aware of their speeds under normal pressure because they meet other molecules and bounce off before they have a chance to go too far. If, however, they find that their way is free of obstacles (as in a near-vacuum), then of course theyll rush unhindered at their dizzying speeds, and thats what will cause the swooshing in the void of the room when the lid is opened. There is nothing mysterious to explain here. Practically the same phenomenon appears when you open a soda can: the great difference in pressure between the molecules of CO 2 in the can (highly pressurized) and the molecules of air outside (in lower pressure) causes the CO 2 molecules to swoosh out of the can and disperse in the air (especially if you have shaken the can and thus increased the internal pressure, hence the speeds of the CO 2 molecules). Same phenomenon. The vacuum, or the low pressure, simply speeds up the rate at which the molecules disperse. The following simulation shows precisely that (click on ): Here, the simulated molecules make longer jumps before they bounce, as they would if they could move in a relatively empty space. The result is the explosion that you see when you run the program, and the much faster filling up of the available space. Now lets turn our attention to the thermodynamic case (hot stone thrown in cold water), because that is what professor Lambert and others dispute as having any relation with the case of configurational entropy. When a hot stone is placed into cold water the molecules of the water acquire energy (well see what that means) and vibrate more vigorously. But because they are molecules in a liquid, they can disperse in the volume of the rest of the water. I prefer to avoid this dispersal of molecules in our thought experiment, because I want the thermodynamic case to appear as different as possible from the previous experiment with the gas molecules in a container that disperse in a room. So Ill propose a small modification in our thermodynamic setup an improvement, actually. Suppose that instead of water we have a piece of concrete. This concrete chunk has a square-shaped hole at its center, and the hot stone is another piece of concrete, which goes and fits neatly and perfectly () into the square hole. Hot concrete goes and fits into the hole of cold concrete, thats all Im saying. (Our figure, below, remains identical: suppose the black area is the cold concrete, and the red is the hot piece.) Now there can be no dispersal of molecules, and yet the second law of thermodynamics guarantees that the smaller hot piece will cool down, the larger surrounding chunk will warm up, and the two will come to a point of thermodynamic equilibrium after a sufficiently long interval of time. The earlier figure is repeated below, for our convenience. Lets think now: how does that happen What is the mysterious energy that flows out of the hot piece What does it consist of How does it flow and why does it disperse In this section well see the correct explanation of how energy (or heat) disperses, and in the next section well review some bogus explanations that have been proposed by others. When the red-hot piece of concrete is placed in the square hole in the middle of the cold chunk of concrete, what kind of interaction can occur between the two bodies at the molecular and quantum level Well, what we know is that some of the vigorously vibrating molecules of the red-hot piece (those that are at its outermost region, its periphery), come into contact with molecules of the cold piece. But contact is not the right term when we talk about molecules, since touching is something that makes sense only at the macroscopic level. At the micro scopic level, the atoms of some of the hot (vigorously vibrating) molecules will approach the atoms of some of the cold (less vigorously vibrating) molecules. Fine, so atoms will approach atoms. Again, atoms cannot touch each other microscopically, so when we speak of an approaching at the atomic level we mean that the electrons of the outermost shells of those atoms will come close together (always while in vibration). So what happens when electrons approach electrons Quantum theory says that electrons that come close together exchange virtual photons. If the electrons were free in space, they would scatter at random angles after this exchange. Now that they are bound to the nuclei of atoms by means of the electromagnetic force, most probably they will continue being bound to their atoms, but their mutual bouncing off will cause their respective atoms to bounce off, too. (This mutual repelling due to the electromagnetic force is the reason that solid objects like ourselves stay on top of other solid objects, like chairs and floors, and do not pass through them.) What interests us is that because one of the two electrons (assume only two of them interacting, for simplicity) moves faster in space than the other one (because it follows the vibrations of the atom it belongs to, which is hotter than the other one), quantum theory says that there is a higher probability that virtual photons will go from the fast-moving electron to the slow-moving one, so that the former will lose some of its energy, whereas the latter will gain some. As always in the quantum world, we talk about probabilities, not deterministic events. But what concerns us is the average case, and on average the fast-moving electron will send one or more virtual photons to the slow-moving one. This is one mechanism by which the mysterious energy is transmitted from one material to the other: this kind of energy is a flow of virtual photons, which cause the electrons hence their respective atoms to recoil. Ale jest coś więcej. The hot piece is depicted in red color on our drawing, right And in reality, red-hot things are, well. red. They are red for the following reason. Their highly excited electrons spontaneously drop to lower-energy levels, emitting photons as they do so. (Real photons, not virtual ones.) The more excited the electron, the higher the probability that the photon will have a small wavelength (high energy). Higher energies mean photons with wavelengths possibly in the visible range, such as in the red part of the electromagnetic spectrum (and even further toward the orange and smaller wavelengths, depending on how hot the object is). As the hot body cools down (we havent seen yet how), the emitted photons are of longer wavelengths, and so are shifted toward the infrared. Thats why the red-hot piece becomes first dull-red as it cools down, then its color fades more, until essentially all the emitted photons are in the infrared, so we dont see them anymore (consequently we see the natural color of the body at lower temperatures, be it black or gray, whatever is reflected by ambient light). As I mentioned, these emitted photons are not virtual but familiar photons that would be registered by our retinas if we could see them. But we cant see them because they are in the closed system of the two concrete pieces of our experiment. So they are emitted within the molecules of the material, and cant go too far because these are chunks of concrete we are dealing with, and concrete is opaque to light (less so to infrared photons, but still relatively opaque). So the emitted photons travel short distances before being absorbed by electrons of neighboring molecules, which they might excite and cause to jump to higher energy levels. Then those excited electrons might emit a photon again and drop back to a lower energy level. The photons are emitted at random angles. So, although we cant talk about the same photon moving from molecule to molecule (or from atom to atom, or from electron to electron), the net result of all this is that there is something like a random walk of photons . Hmm. a random walk. This is clearly the case with normal photons. But the virtual photons, too, do something analogous, because they are also exchanged between electrons at random angles. So this is what the mysterious flow of energy is: its photons that perform random walks. Energy in the context of our experiment is not a substance made of some mysterious and otherworldly material, but a convention for the wavelength of photons: the shorter the wavelength, the higher the energy. At a macroscopic level its often useful to model energy by the quantity of an abstract substance (e. g. temperature), because this allows us to solve conveniently problems about objects and processes in the macro-world. But down at the microscopic level of description, in our thermodynamic experiment, energy is associated with the wavelength (or frequency) of photons, i. e. photons that, as I said, perform random walks (or behave as if the same photon performs a random walk). () Therefore, random walks are the reason why energy disperses within the cold body until there is an equilibrium, and the dispersion theorem models the situation. And this discussion tells us that the two figures that were juxtaposed at the top of this page essentially simulate the same phenomenon: the figure on the left (the two blocks of concrete) shows the situation macroscopically, with photons performing random walks and dispersing within the material and the figure on the right shows the situation microscopically, depicting individual molecules of a fluid that perform random walks and disperse in a box. In the latter case, what we have is the dispersal of matter. In the former case we are tempted to say that we have the dispersal of energy but the reason I keep putting the word energy in quotes is because I want to emphasize that even in this case we still have the dispersal of matter. For, is a photon immaterial Of course not, its a little lump of matter in the generalized sense, the sort of massless matter that we prefer to identify with energy (but which can be assigned a non-rest mass m through the relation m E c 2 , where E is the energy of the photon). The useful distinction that can be made is that the configurational case involves the dispersal of matter in the form of mass, whereas the thermodynamic case involves the dispersal of matter in the form of energy . But, by whatever name and form it goes, generalized matter disperses in spacetime when its quanta perform random walks, and the reason is not physical, but mathematical, given by the dispersion theorem. Note please: when I say the reason is not physical I dont mean its supernatural I mean that the laws of physics as we know them (including Newtons laws of motion, quantum mechanics, and everything we know about the four forces of nature), do not suffice to explain the reason for the average dispersal of random-walking particles. An extra-physical, a mathematical result is needed to explain this phenomenon. Of course, if we include this mathematical result into the notion laws of physics, then we can again say that the laws of physics in this inclusive sense explain fully the phenomenon. () I hope the above discussion explains sufficiently the claim that I made earlier: the two entropies, thermodynamic and configurational (and even the third kind that I briefly referred to as virtual earlier), are manifestations, or implementations, of a deeper mathematical result. The second law of thermodynamics () is, similarly, at work whether we talk about energy or mass dispersing in spacetime. Consequently, the drive to eliminate references to configurational entropy in American chemistry textbooks is utterly meaningless it actually disseminates knowledge superficially to students because they dont see the deeper mechanism that is responsible for material dispersal, but only one aspect of it, as it appears in the thermodynamic case. However, although the relation between thermodynamic and configurational entropy is unassailable, there is still confusion about the role of order and disorder in this context. The Confusion Let us see a couple of explanations for the second law of thermodynamics that have been given, which ignore the dispersion theorem and the deeper relation between thermodynamic and configurational entropy. First, consider the configurational case, and Brian Greenes explanation for why molecules (or other material things in general) disperse in space. Greene first presents the notion of entropy by asking the reader to imagine tossing an unbound copy of Tolstoys War and Peace high into the air, letting the 693 double-sided loose pages drop on the ground, and then collecting them one by one, without looking at their page numbers. What is the probability that the pages will be collected in their correct order Greene calculates that there are about 10 1878 different out-of-order page arrangements (and presents the entire 1878-digit number using the better part of p. 152 of his book). He observes that there is only one correct (or desired) order, so the probability to pick up the pages in the correct order and keep reading about Anna Pavlovna and Nikolai Ilych Rostov (and understanding what is being read) is about 110 1878. i. e. vanishingly small. Jak na razie dobrze. Now lets see how he explains a more typical experiment that is often described in the context of entropy and the second law of thermodynamics. Consider opening a bottle of Coke. (Any other plastic soda bottle or other type of plastic bottles wholesale may be used too.) Gas, like CO 2 . is initially confined in a small space in the bottle. After we open the cap of the bottle, the molecules of CO 2 spread evenly in the room. Here is how Greene explains this: When you twist off the bottles cap . you open up a whole new universe to the gas molecules, and through their bumping and jostling they quickly disperse to explore it. Why Its the same statistical reasoning as with the pages of War and Peace. No doubt, some of the jostling will move a few gas molecules purely within the initial blob of gas or nudge a few that have left the blob back toward the initial dense gas cloud. But since the volume of the room exceeds that of the initial cloud of gas, there are many more rearrangements available to the molecules if they disperse out of the cloud than there are if they remain within it. On average, then, the gas molecules will diffuse from the initial cloud and slowly approach the state of being spread uniformly throughout the room. Thus, the lower-entropy initial configuration, with the gas all bunched in a small region, naturally evolves toward the higher-entropy configuration, with the gas uniformly spread in the larger space. In The Fabric of the Cosmos, pp. 155156. But there is a glitch in the above explanation. Okay, the initial gas cloud is confined in a smaller space than the space of the entire room. But why would a molecule choose to move away from the cloud What pushes it there, to the rest of the room One might counter, the highly pressurized state of the gas in the bottle pushes it, i. e. the vigorous bumping and jostling with the other molecules of the gas cloud. Yes, but we dont have to imagine a pressurized gas. The same phenomenon will be observed if the pressures of the gases inside and outside the bottle are identical: still the gas-inside will spread in the rest of the room. So, again: what pushes molecules to explore the rest of space, as Greene puts it, even under a lack of pressure differential Merely because there are many more rearrangements available to the molecules if they disperse out of the cloud than if they remain within it is not an explanation, because molecules dont care about numbers of rearrangements and opportunities given to them to explore some terra incognita they merely move randomly in space For all we know (if we ignore the dispersion theorem), they could be roaming forever around their original location, and thus staying within the gas cloud. Greene comes close to the qualitative explanation given earlier on this page (Im referring to the figure of the colored red-and-green circle, just before the theorem), but he doesnt quite put his finger on it. Greene gets distracted (and distracts the reader) with the pressure differential, instead of concentrating on an example with a lack of such differential. If I shoot a bullet with a gun against a target, it should be of little wonder if I see the bullet hitting the target but if I simply take a bullet in my hand, then let go, and see it floating away from my fingers, then I am confronted with a phenomenon that requires a nontrivial explanation. Next, consider the thermodynamic case and Prof. Lamberts crusade to purify American chemistry textbooks from the configurational blemish by severing the relation between thermodynamic and configurational entropy, making reference only to the thermodynamic case in serious, scientifically approved textbooks. Lambert attempts to explain the second law of thermodynamics (i. e. the statistical increase in thermodynamic entropy) in this web-page by means of a dialog between a Professor (presumably himself) and an imaginary Student (perhaps his alter ego: a bombastic individual that should serve as an example of how students should not behave if theyre really interested in learning, as opposed to showing off their knowledge). Here is the Professors explanation of the microscopic reasons why energy disperses in space. First, the Professor observes that molecules of water (he uses water as a typical example) move in three different ways or, better stated, their motion has three degrees of freedom, or components: a translational component by which they change their location in space a rotational component, by which the entire H 2 O molecule rotates around some axis (which can change in time) and a vibrational component that concerns the bonds between OH atoms within the H 2 O molecule, by which the distance between such bonds periodically increases and decreases (extremely fast by our human temporal standards, of course). The following figure is from the above-referenced web page, and shows the three motional components for a water molecule. What the Professor never states explicitly in his discussion with the Student is the obvious observation that, of the three components of molecular motion, only the translational one can be suspected (held responsible) for the dispersal of energetic molecules in space. Clearly, no matter how fast a molecule rotates, or how fast the bonds between its atoms vibrate, it will not be translated in space. Thus two-thirds of the Professors description of molecular motion are irrelevant for the purposes of explaining dispersal. Then the Professor goes on to explain to the Student how each of the three motional components is quantized, i. e. there are only specific and discrete values for the angular momentum of the rotational component: its not that the molecule can change its rotational speed along a continuum of values. The same is true for the vibrational and translational components. The Professor observes that the available quantized (discrete) values of the translational component are way more (really-really way more) in number than the possible discrete values of the rotational and vibrational components. But since the latter two are irrelevant for the explanation of dispersal, I will ignore this distinction in the numbers of quantized values. Now comes the crucial part in the Professors explanation. He says, take a snapshot of the current state of motion of the water molecules. Call this a microstate . Thus, in a given snapshot, the translational component of molecule 477,275,846,375,832,218 has a certain value (I said Ill ignore the other two components) its neighboring molecule 477,275,846,375,832,219 has a different translational component and so on. Collect all those components for all the zillion molecules in the quantity of water under consideration, and you have your microstate . Here it is, in Professors own words: Imagine that you could take an instantaneous snapshot of the energy of all the individual molecules in a flask containing a mole of gas or liquid at 298 K. Remember that each molecules energy is quantized on a particular energy level. Then, each of the far-more-than Avogadros number of accessible energy levels (at that temperature and in that volume) could have zero, one, or many many molecules in it or on it. The whole snapshot showing each molecules energy of that mole is called a microstate the exact distribution on energy levels of the energies of all the molecules of the mole at one instant in time. Now consider what will happen next (says the Professor). The first of the above molecules will bounce against another one (usually a neighboring molecule, since this is water and its molecules cant move too far before being hit by others) and will change its translational component. But there are many available options for the new value of its translational component. And this is true for all molecules in the fluid. Therefore, over time, the molecules will explore the space (note: the abstract space, says I) of possible values of their translational components. Hence well end up with microstates that have their translational space widely distributed, as opposed to the single initial microstate. In Professors words: Since a collision between even two molecules will almost certainly change the speed and thus the energy of each one, they will then be on different energy levels than before colliding. Thus, even though the total energy of the whole mole doesnt change and even if no other movement occurred that single collision will change the energy distribution of its system into a new microstate Because there are trillions times trillions of collisions per second in liquids or gases (and vibrations in solids), a system is constantly changing from one microstate to another, one of the huge number of accessible microstates for any particular system. Then the Student asks a crucial question: What does more microstates for a system have to do with its energy being more spread out A system can only be in ONE microstate at one time. And the Professor answers as follows (my emphasis ): Yes in only one microstate at one instant. However, the fact that the system has more choices or chances of being in more different microstates in the NEXT instant if there are more microstates for the system is the equivalent of being more spread out or dispersed instead of staying in a few and thus being localized. . You i. e. the Student already stated the most important idea, a single microstate of a system has all the energies of all the molecules on specific energy levels at one instant. In the next instant, whether just one collision or many occur, the system is in a different microstate. Because there are a gigantic number of different accessible microstates for any system above 0 K, there are a very large number of choices for the system to be in that next instant. So it is obvious that the greater the number of possible microstates, the greater is the possibility that the system isnt in this one or that one of all of those gazillions. It is in this sense that the energy of the system is more dispersed when the number of possible microstates is greater there are more choices in any one of which the energy of the system might be at one instant less possibility that the energy is localized or found in one or just a dozen or only a million microstates. It is NOT that the energy is ever dispersed over or smeared over many more microstates Thats impossible. So, what does energy becomes more dispersed or spread out mean so far as molecular energies are concerned Simple Whats the absolute opposite of being dispersed or spread out Right completely localized. In the case of molecular energy, it would be staying always in the same microstate. Thus, having the possibility of a huge number of additional microstates in any one of which all the systems energy might be in thats really more dispersed at any instant Thats what an increase in entropy on a molecular scale is. Więc. lets see. Suppose I have a marble ball in my hand, and there is a number of holes on the ground at a distance of about one yard from me. Each hole is large enough to let the marble fall inside, and suppose at most one marble can fit in each hole. I throw the marble forward, letting it roll on the ground toward the holes. Following the Professors logic (see the highlighted portion, above, and match it with what follows), although the marble can be in only one hole at one instant, because there is a large number of different accessible holes, there are a very large number of choices for the marble to be in that next instant. So it is obvious that the greater the number of possible holes, the greater is the possibility that the marble isnt in this one or that one of all those holes. It is in this sense that the positional state of the marble is more dispersed when the number of holes is greater. Does it make any sense No, not to me. A marble can be in one hole at a time, period. How can its potential for choosing from among a large number of holes send it to more than one hole And if you think the analogy with a single marble (single molecule) is misleading, okay, think of 10 marbles. Throw them forward, as before. Arent they going to end up in exactly 10 different holes Now take those 10 marbles out of their holes, step back, and throw them forward again. Arent they going to end up again in exactly 10 different holes 10 different holes, in general, to be sure. But why would the marbles disperse among the holes Unless, of course, we modify the marblesholes experiment as follows: perhaps after we remove each marble from its hole we dont step back, but place the marble just next to its hole, and give it a little kick toward a random direction. The marble then goes and falls into a neighboring hole. Then we continue like that, taking it out, and giving it another kick to a random direction. Then, the marble will perform a random walk, and the dispersal theorem tells us that if we repeat this many times, on average the marbles will disperse. But this modification cannot apply to the Professors energetic molecules, and here is why: Each molecule has a given value for its translational component, right Thats a given value for its kinetic energy level . (Note the KE in Prof. Lamberts figure, above: it stands for kinetic energy.) So it is reasonable to imagine that any given molecule changes its energy level with each kick that it gets from other, neighboring molecules. Its energy value performs a random walk in the abstract space of quantized kinetic energy levels. But why would this kind of random walk in the abstract energy space imply that the molecule will perform a random walk in physical space This is like saying that a person who is some times happier than other times (i. e. performs a random walk in an abstract happiness space) is expected to visit more places in the world than another person who stays at the same happiness level all the time. Why It doesnt compute. Its a non sequitur. The translational components of the moving molecules can indeed acquire many different values, i. e. kinetic energy levels. But it is not obvious at all that this will cause the energy of the molecules to disperse in physical space not unless we take into account the dispersal theorem, and the observation that, in the context of our experiment, energy is transmitted through photons, which are the agents that perform the random walks, from electron to electron. (It is interesting that the word photon does not appear even once in Professor Lamberts microworld explanation of energy dispersal.) What about order and disorder Prof. Lambert makes it very clear that all talk about order and disorder in the context of entropy and the second law of thermodynamics is wholly unjustified, an example of sloppy thinking, a Cracked Crutch For Supporting Entropy Discussions . This, in spite of the fact that well-known authors such as Hawking, Greene, and Davies (among others) seem to feel no compunction to talk in terms of order and disorder, as shown in the excerpts at the beginning of this page. Prof. Lambert begins as follows in the above-referenced article: To aid students in visualizing an increase in entropy many elementary chemistry texts use artists before-and-after drawings of groups of orderly molecules that become disorderly. This has been an anachronism ever since the ideas of quantized energy levels were introduced in elementary chemistry. Orderlydisorderly seems to be an easy visual support but it can be so grievously misleading as to be characterized as a failure-prone crutch rather than a truly reliable, sturdy aid. Prof. Lambert later proceeds with an example that, according to him, shows why the talk about order and disorder is a cracked crutch. He asks the reader to imagine a bowl with water and chunks of ice floating on its surface, (figure below, on the left). After some time, the ice has melted and the bowl contains just water in liquid form (figure, on the right). Ice floating on water in a bowl (left), and same bowl with plain water after ice has melted away (right) People who are being introduced to the notion of entropy perceive the water-plus-ice-chunks as a disorderly collection of objects, says Prof. Lambert, whereas they perceive the later plain water as a uniform substance, an ordered form. So they might think we have a counter-example here: a disorderly collection of objects turned into an orderly soup. So they get confused (he claims). Yes, I agree that people would get confused if what is order and what is disorder in a situation such as the above is described to them in the manner suggested by Prof. Lambert. But thats a wrong description. Learners can always be confused with wrong descriptions. A good educator must explain things in the right way. The order in the bowl with the floating chunks of ice is to be found in the configurations of H 2 O molecules that form the ice crystals within each chunk of ice. There are many fewer configurations of molecules that form ice crystals in chunks (thats order) than configurations of molecules that float free in the soup of pure water (thats disorder, see more below). So, having heard the proper description, the learner will see an order-to-disorder progression and no contradiction with the 2nd law of thermodynamics. This is not a unique case of an initially wrongly formed perception due to intuition. Without proper tutoring in physics, people tend to think that heavy objects fall faster than light ones even Aristotle was fooled on this one that the Sun turns around the Earth once every day, and that mass is identical to weight. But a wrong first impression cannot be a reason for abandoning the more informed physical description. Why do we say there is more order in the bowl with the floating ice, and less order (or more disorder) in the bowl with the plain water Because the former situation is analogous to the molecules of a gas being restricted in a small volume, as in the examples discussed earlier in this text, whereas the latter situation is analogous to the gas molecules being spread out everywhere in the available space (see figure, below). Ordered molecules, akin to ice crystals floating on water. Molecules in disorder, akin to a soup of molecules in liquid water. There is a subtle issue, however, when we say that the image on the left, above, is more ordered. The way I arranged the molecules (dots) in a square 10 x 10 grid, of course appeals to our sense of order. But why How can we make the notions order and disorder precise, so that even Prof. Lambert (and like-thinking scientists) will have no reason to claim that orderdisorder is not an un-physical notion, a mere psychological thing, a cracked crutch for the understanding of entropy What can be made precise are not exactly the notions of order and disorder, but the very closely related notions of compressible and incompressible configuration. The reason is this: to say that the molecules of the image on the left, above, are ordered we need the judgment of a person, who would notice that the molecules are arranged in a perfect matrix of 10 rows by 10 columns. I might have arranged the molecules in a diamond-like shape, or along the circumference of a circle, or make the 100 dots form 20 crosses of 5 dots each and place the crosses themselves on 4x5 matrix, or arrange them in an essentially unlimited number of other ways. In each such case, a person with enough intelligence and patience might see the pattern, and come up with a short description of the 100 dots. The person might, or might not see the pattern of dots that I selected, depending on how difficult the pattern would be. In some difficult cases the person might fail to discover the pattern. Consider for example the picture on the right, above. It might be that I placed the dots on such x, y coordinates that the expression xy 1 is a prime number. I didnt, but I could have done so. And nobody can guarantee that a person would succeed in discovering that relation. If a relation for the position of dots (a pattern) is discovered, we say the configuration can be compressed . The notion of compression refers to the fact that the configuration of dots can be described in a short way (e. g. 20 crosses of 5 dots each) otherwise we say the configuration is incompressible . But the subtle issue is: if it is incompressible, is it so because nobody succeeded in compressing it (although there might be some yet unknown way), or because there really isnt any way to compress it, even if God so to speak, i. e. a super-intelligent being attempted to do it The notion of incompressible information is directly related to the notion of randomness . We can think that the dots on the right-side figure, above, are randomly placed . Disordered, randomly placed, incompressible all these notions seem to refer to the same concept. But some mathematicians, physicists, and philosophers, would say that randomness (a. k.a. incompressibility, a. k.a. disorder), cannot be defined, because we can never know if a configuration of things (dots on the plane, numbers in a sequence, etc.) defies any description through a rule (making it patterned, or compressed, or non-random, etc.), or it just happens that no human being (or computer algorithm, etc.) has succeeded in compressing it yet. Since we cannot always know, they say, we dont have a definition. For instance, the physicist Heinz Pagels says the following: Andrei Kolmogorov, the great Soviet mathematician, thought he could define randomness by the criterion that if it took as long to state the rule, suitably transcribed into numbers, for the construction of the numerical sequence as the actual length of the sequence, then the sequence was random. However, finding the construction rule for the sequence depends on human cleverness, and we can never be assured that the rule we have found is the simplest one that gives the sequence. . A precise definition of randomness for finite sequences simply does not exist. In The Cosmic Code, 6 pp 8687. And yet, I want to make a proposal for avoiding this trap (the trap of not knowing whether a human might succeed compressing the configuration), and propose an objective mechanism that can serve as a definition of randomness (and of incompressibility, and of disorder, etc.). Take a very specific compression algorithm, as implemented in programs that zip our computer files. I have and use WinZip v. 8.1 on my PC, but the particular implementation is not important whats important is the algorithm . Suppose the algorithm is fixed once and for all, for this definition of randomness, and we disallow any tinkering with it otherwise we must understand that we tinker with our definition. It suffices that the algorithm does a pretty good job in attempting to compress any file (which is merely a sequence of bytes, i. e. numbers). Having fixed the algorithm, my definition of randomness is a function that takes as input any sequence of numbers (which can also be the coded form of a configuration of dots, or molecules, in space), and outputs a number in the interval 0, 1), which is proportional to the percent of compression achieved. (Divide the percent by 100 to convert it to the interval 0, 1)). The parenthesis after 1 means that the number can never be exactly 1, because that would mean the sequence would vanish completely, and such total compression is inconceivable. But the closer the number is to 0, the more random the input sequence is. The bracket before 0 means that a compression of exactly 0 is possible, and it means No compression at all was achieved. (OK, I admit the above definition of randomness is not useful at all for theoretical math purposes, since it relies on a commercial algorithm or on some compression algorithm in general, a specific one and so it is algorithm-dependent. But my purpose wasnt to provide a theoretically useful definition, but to show that a definition can exist, its simply not true that randomness is an indefinable notion.) Thus we see that, in this definition, random is not a black-or-white notion (its not that a sequence either is random or is not), but has a gradation: a sequence (or configuration) can be more random than another one, which can in turn be more random than a third sequence, and so on. Nor does the definition require human cleverness, since it is all done by a fixed algorithm. Of course, an intelligent human might come and say, Now look, this sequence that you declared quite random is really quite compressible, thus not as random as you think, because I can use the such-and-such rule by which it is compressed quite a lot. W porządku. That means merely that the said person did not abide by our definition, but used a different approach, a different algorithm for achieving compression. One can always imagine a different algorithm. For instance, consider again the disordered dots on the right-side of the most recent figure (or the one below). One can state that the coordinates on which those dots stand are precisely the coordinates that, in that persons numbering of coordinates, correspond to an N x N matrix, and thus the dots are perfectly ordered. The person altered the algorithm by which we number coordinates, and thus arrived at a non-random configuration. But thats not impressive at all. The point is, given a fixed compression algorithm, how much can a sequence be compressed The less it is, the more random it is declared to be, with respect to the given compression algorithm. To be meaningful, the above definition depends on the assumption that the algorithm indeed performs reasonably well in compressing its input. But most commercial algorithms do have this feature. For example, consider the following three snapshots from our molecule-dispersal simulation: I started with an initial number of 50 x 50 2,500 dots. Snapshot (a), on the left, is taken shortly after the beginning, snapshot (b) a little later, and snapshot (c) well after the dots occupied the entire space. The original uncompressed size of each of the three images (i. e. stored as bit-mapped files) was 441,654 bytes. After compression with WinZip, the files acquired the following sizes: snapshot (a): 4,823 bytes snapshot (b): 6,442 bytes snapshot (c): 8,660 bytes Thereafter, any further essential compression was not achievable. So we see that the last of the three snapshots is the least compressible one, and the dots can be said to be the most randomly distributed in it. Note that even the last, least compressible image, is quite compressed in absolute numbers (from 441,654 bytes its squeezed down to 8,660). Thats because the 2,500 dots that I placed in the available space are still too few, and the space ends up having large expanses of emptiness (white color) even when the dots are nearly evenly distributed in it. Had I used 73,600 dots, which is half of the available pixels in the above space, I would end up with an essentially incompressible late snapshot. Also note that I didnt start snapshot (a) at a perfectly ordered configuration (a 50x50 matrix) because I wanted to show that compression is independent of our human conventions about when a configuration is intuitively called ordered. An excellent article describing the relation between randomness, compression, and the 2nd law of thermodynamics (among other fundamental notions) is Gregory J. Chaitins, Computers, Paradoxes, and the Foundations of Mathematics. 7 The article is written for the general educated reader it doesnt contain a single mathematical formula. By the way, in that article, Chaitin writes (my emphasis): Entropy measures the degree of disorder, chaos, randomness, in a physical system. A crystal has low entropy, and a gas (say, at room temperature) has high entropy. str. 169. Professor Lambert gives one more example in his cracked crutch article that requires special attention, and a bit more thought. In his attempt to show that in reality order does not always result in disorder, but the opposite can also happen, he brings up the example of some solutions that start out as a uniform soup, but in the course of time crystals are formed within the soup, and so we get the opposite situation of what I showed earlier, when I discussed the ice-crystals-to-uniform-water example. My most familiar example of this (which in fact I demonstrated to my daughters several years ago, as part of their world-of-nature education) is to dissolve as much salt as you can in water (resulting in a saturated solution) and then hang one or more little threads from the top, so that the tips of the threads are immersed in the solution. After about one day, cubic crystals of salt will form on the threads in the solution, and the crystals will grow as the days pass. So, there you have it: a disorder to order demonstration The subtle but essential difference of this experiment with what we have been discussing so far is that the molecules of water and salt in the solution do not perform random walks . Instead, there are inter-molecular forces between the molecules of the threads and the salt molecules that cause the latter to go and attach themselves on the former. Then more molecules of salt come and attach themselves on top of the previous ones. Salt has the property of forming cubic crystals in its solid state, so we see the crystallization of salt along the threads. If we do not allow material objects to perform random walks, then of course we can get around the order-to-disorder rule. This is precisely what natural selection has been doing on our planet for billions of years. Thats why we ended up with so many biological crystals, such as elephants, oak trees, human brains, and even the lowly bacteria. Even if the Earth-Sun system were a thermodynamically closed system (which it isnt), still evolution could occur and result in exquisite biological crystals, because molecules on Earth are not allowed to perform random walks, but obey an untold number of lawful (non-random) interactions due to chemical processes (and later due to biological, and later due to cognitive processes). Prof. Lambert is distracted by these non-random events, because in the thermodynamic case (where energy disperses) there isnt anything that can serve as an attractor of the carriers of energy, i. e. of photons, and force them to form photon crystals. When photons are let loose, loose theyll go, and there is nothing to keep them from spreading at least not anything in our immediate experience. But our imagination does not have to be limited by our immediate experience. Its possible to imagine a world in which even photons get trapped. For instance, imagine a small universe with a single regular star. The star has been shining for quite some time, so its photons have dispersed practically everywhere in that small universe. Trillions of years pass, and the star dies, turning to a tiny mass of non-luminous matter that withers away, particle after particle. So there is nothing but a uniform soup of photons in that universe, which of course is assumed to be a closed system. Now suppose we insert a black hole in that universe. (Dont ask me how we do it, by what physical means without violating the laws of physics, because this is not a thought experiment, but an exercise in imagination-gone-wild) What will happen then to the photons (to the energy ) in that universe Will they keep being distributed evenly in space No, because those photons that fall into the event horizon of the black hole will get trapped and disappear forever. Some other photons, in the vicinity of the event horizon, will be disturbed and swerve around the black hole before escaping from it for good, perhaps after first rotating a number of times around it depending on how close to the hole they happened to be. In any case, the even distribution of photons in spacetime will cease to exist. But an uneven distribution of energy, compared to a previously even one, means a decrease in thermodynamic entropy, at least for a while. Violation of the second law of thermodynamics In principle, yes. Unfortunately, the universe that I described is so contrived that we cannot call the above a thought experiment. But it serves to remind us that the only reason that thermodynamic entropy seems to be always increasing in our world is because there are no photon magnets around, so energy does not get trapped, it disperses unhindered, and we observe no violation of the second law. However, mass is different: mass does get trapped, so we observe both its dispersal (when other forces are weak enough to let it roam free) and its accumulation (when other forces take the upper hand). Therefore, configurational entropy, which concerns mass, can be reversed in many situations (such as in biological and material evolution). Another objection that is often raised by those who see an unbridgeable gap between thermodynamic and configurational entropy is that the former is measured in specific physical units: in joules per degrees Kelvin whereas configurational entropy has no such physical units to measure it: its a pure number. The objection goes further in saying that, even that pure number is not definite: it depends on how finely we partition the space in which the molecules (or other carriers of mass, or information) move. Consider first the objection that the thermodynamic entropy is measured in specific physical units, whereas the configurational one is just a number. Well, so what Nobody claims that the two versions of entropy are identical, or even isomorphic. If they were, we wouldnt need to distinguish the one from the other, and there would hardly be any contention among physicists. There are many other examples in physics in which two phenomena are consequences of a deeper law, and there are features that exist in one phenomenon that are measured in some particular physical units, but are absent from the other. For instance, consider the orbit of the Moon around the Earth, and the free fall of an apple toward the surface of the Earth. For a very long time the two phenomena were considered as different as two phenomena could be. But after Newtons era we learned that they are implementations of the same fundamental law, the law of gravitational attraction. Now, in the case of the Moons orbit, there is a specific property called angular momentum L , defined as L r x p , where r is the position vector of the rotating body (for the Moon, this vector has its origin at the point of the center of mass of the system EarthMoon and points toward the Moon), p is the linear momentum of the rotating body (for the Moon, its a vector with origin on the Moon and direction tangential to the Moons orbit), and x is the cross product of the two vectors. L is measured in kilograms times meters squared per second (kgm 2 s -1 ). Now, in the context of the falling apple, there is nothing of all that zoo of properties and units, because the angular momentum is always zero ( r and p turn out to be parallel, so their cross product is zero). So what Does the nonexistence of angular momentum (corresponding to the nonexistence of temperature in configurational entropy) and the irrelevance of the units kgm 2 s -1 in the case of the apple destroy our conviction that both the falling apple and the orbiting Moon represent implementations of a deeper law of physics Then the objection that the value of the configurational entropy depends on how finely we partition the space is also misguided. The value of the thermodynamic entropy varies, too, depending on our units of measurement: it comes to one value if we measure temperature in degrees Kelvin, and to another value if we measure it in degrees Fahrenheit. So what Keeping our units fixed, the important observation is that a later measurement of thermodynamic entropy yields a larger value than an earlier measurement of it, when we measure it in the same closed system. Likewise, keeping our partitions of the space fixed, a later measurement of configurational entropy yields a larger value than an earlier measurement of it, assuming the particles (or carriers of information) perform merely random walks, and no attracting forces are applied to them. What is important in both cases is that we have a fixed scale that yields values in total order, () so that we can compare measurements, and the results of the comparisons be consistent with the total-order relation. Prof. Lambert, and others whose papers he references, mock at examples like the following: a college student organizes their closet, so objects appear to be orderly in it for a while. After a few weeks, or months, things in the closet look just as disorderly as before the organizing attempt. This, according to Prof. Lambert, is a completely flawed application of the second law of thermodynamics, and an example of how wrongly the fundamental notions of physics, such as entropy, can be perceived by beginning students. And yet, there is something in this example that, once again, escapes from Prof. Lamberts horizon. The reason is that this is an extra-physical example, one for which the low physical level with its laws is insufficient to explain fully. Its not that there is anything non-physical (immaterial) in this example, but that the laws of physics as we know them simply do not suffice for its full explanation, just as they do not suffice for the explanation of biological phenomena (and thats why we have biology and dont resort to quantum mechanics to explain evolution), or for the explanation of cognitive phenomena (thats why we developed psychology and cognitive science). There are plenty of examples showing that a higher level of material organization has copycated phenomena and principles that hold at a lower level, and the objects-in-the-closet case is just one of them. Consider another, more familiar one: the notion of force. Forces are understood literally by physicists as those interactions that result in the attraction or repelling of material objects: the strong force, the electromagnetic force, and so on. () But there are also biological forces, such as those that keep the fish of a school close together, so that the fish dont disperse in the water and dont go each its own way. Such forces can definitely be reduced to the low-level physical ones, but the reduction is not trivial. Further, there are psychological forces, such as when two people feel attraction that causes them to stay close together and form a family. Again, the reduction first to biological, and then to physical forces exists, but is nontrivial. A similar case could be given for the notion of wave: there are physical waves (e. g. of electromagnetic nature), natural waves in the macro-world (sound waves, water waves), but even social waves, such as waves of fashion and of culture. The more detached from low-level physical reality a notion is, the more prone it is to become the target of ridicule by some physicists who think that the real thing is the object of their study, and everything else is there by mere analogy and sloppy thinking by laypeople. But theyre wrong. The material world has become more complex than what physics can conveniently describe. It can be shown that even though phenomena are in principle reducible to the lowest, quantum level (in the sense that no mysterious immaterial forces or magic is needed for them to occur), there are some that cannot be reduced in practice . For example, the problem of figuring out how two people are attracted to each other (and stay close by the force of love) is not necessarily solvable in terms of quantum physics. (It might be, I am only surmising.) A similar case might be the objects-in-a-closet example. The student goes and puts objects in order, but what happens thereafter is random walks (figuratively speaking) of the objects, because forces that move them are applied to them, and such forces do not have the order as an objective, but are of varying strength and random directions (as far as the order in the closet is concerned). So we get disorder. Hard to translate to low-level physical language, but not completely irrelevant to it. Such analogies from higher levels of material organization are not completely useless, contrary to what Prof. Lambert believes, because they help the beginner relate to something familiar before plunging into the more unfamiliar, low-level physical situation. The Conclusion We saw that each of the two implementations of the dispersion theorem, the thermodynamic and the configurational case, depend on the quality of the material dispersed: when the material quality is energy, we deal with thermodynamic entropy and the notion of heat whereas when the material quality is mass, we deal with configurational entropy and the notion of orderdisorder (or in-compressibility, or randomness). We also saw the mathematical explanation, or justification of the second law of thermodynamics, through the dispersion theorem . One important difference between the two implementations is that, in our familiar corner of the universe, energy is nearly impossible to contain, to keep from spreading. As a result, we observe the familiar thermodynamic notion that, no matter what, energy will disperse in space-time. Whatever feeble attempts we make to contain it fail: if we try to concentrate energy, well spend more energy to achieve the concentration than the energy well collect, and so we conclude that entropy increases inexorably. But with mass its different. Objects with mass can be disallowed from performing random walks. When that happens, we observe a reversal in the increase of configurational entropy, which we interpret as an increase in order, or a decrease in randomness and chaos. One familiar and very important case of decrease in configurational entropy is the biological evolution on our planet, and even more generally of material evolution: considering the original primordial soup of quantum particles, which was the state of the universe shortly after the Big Bang, and the later lumpy texture of it (clusters of galaxies, galaxies, stars, etc.) created by gravity, we see that, although thermodynamic entropy increases in the universe (assuming it is a thermodynamically closed system), its configurational entropy probably decreases on a large scale, primarily due to gravity, but also due to the other attracting forces of nature. For corrections, suggestions, comments, etc. consider contacting the author. Hawking, Stephen W. (1988). A Brief History of Time. New Work: Bantam Science. () Greene, Brian R. (2004). The fabric of the cosmos: space, time, and the texture of reality . New York: Knopf. ()Davies, Paul (1995). About Time . New York: Simon amp Schuster, a Touchstone Book. ()Einstein, Albert (1956). Investigations on the Theory of the Brownian Movement. This posthumous publication of Einsteins five papers on Brownian motion is translated by A. D. Cowper, and edited and annotated by R. Frth. Dover Publications. ()Weisstein, Eric W. (1999). CRC Concise Encyclopedia of Mathematics. CRC Press. ()Pagels, Heinz R. (1983). The Cosmic Code: quantum physics as the language of nature. New York: Simon amp Schuster, a Bantam Newage Book. ()Chaitin, Gregory J. (2002). Computers, Paradoxes, and the Foundations of Mathematics. American Scientist, v. 90, MarchApril 2002, pp 164171. () Footnotes: (Clicking on the footnote number brings back to the text) () The thermodynamic entropy S is defined by the relation S Q T, where Q is the amount of heat absorbed in a reversible process, and T is the absolute temperature at which the process is occurring. Conceptually, thermodynamic entropy is the amount of energy that cannot be used to do useful work, the useless energy. () Take this perfectly as an idealization. Weve made other idealizations, too, such as that we always deal with perfectly closed systems, therefore this is not the only one. () The same convenience of thinking leads us to treat electricity as a substance in the macroworld, or as a fluid that flows within objects and yields an electrical current. But we know that, in microworld terms, this is only the emergent statistical result of a vast number of particles (electrons) that move within the atoms of the material. () Alternatively, we can think of physics as nothing but mathematics, down at the lowest level of description. Therefore, every mathematical result can be considered as potentially part of physics, in this view. Indeed, theoretical physicists often express the view that when the world is examined at its most fundamental constituents, human-made notions and reality disappear, and what remains is only describable by mathematical equations. () Thus the term Second Law of Thermodynamics is somewhat misleading, because it refers only to one manifestation of a deeper law: the thermal manifestation, where what disperses is energy through photons. People seem to use this term to refer even to the deeper law, for which there should be another term, such as The Law of Dispersal, in which the entity that disperses can be energy as in the thermodynamic case, or matter as in the configurational case, or even abstract information, as in the virtual case. () Total order is a mathematical notion that refers to a set in which any two of its elements x and y can be compared, and the result of the comparison is either that x lt y, or that x gt y, and if both x lt y and x gt y then it must be that x y . The relation must also be transitive, see here . () There are four low-level (physical) forces in nature, agreed upon by all physicists now (early 21st C.): the strong, the electromagnetic, the weak, and the gravitational interaction. A fifth force has been stipulated, believed to be responsible for the expansion of the universe, but its status as a force is currently debated. Naples, Florida Mean prices in 2018: All housing units: over 1,000,000 Detached houses: over 1,000,000 Townhouses or other attached units: over 1,000,000 In 2-unit structures: over 1,000,000 In 3-to-4-unit structures: 682,936 In 5-or-more-unit structures: 839,004 Mobile homes: 44,474 Median gross rent in 2018: 1,225. Profile lokalnych firm Umieść swój profil działalności BampM tutaj bezpłatnie. 50,000 businesses already created their profiles Business Search - 14 Million verified businesses Races in Naples, FL (2018) 18,990 88.0 White alone 1,139 5.3 Hispanic 1,030 4.8 Black alone 174 0.8 Two or more races 86 0.4 Asian alone 28 0.1 Other race alone 15 0.07 American Indian alone Mar. 2018 cost of living index in Naples: 105.3 (more than average, U. S. average is 100) Recent articles from our blog. Nasi pisarze, wielu z nich doktorat absolwenci lub kandydaci, tworzyć łatwe do odczytania artykuły na różne tematy. Recent posts about Naples, Florida on our local forum with over 2,000,000 registered users. Naples is mentioned 6,602 times on our forum: According to our research of Florida and other state lists there were 229 registered sex offenders living in Naples, Florida as of February 25, 2017 . The ratio of number of residents in Naples to the number of sex offenders is 88 to 1. Median real estate property taxes paid for housing units with mortgages in 2018: 5,163 (0.5) Median real estate property taxes paid for housing units with no mortgage in 2018: 4,713 (0.6) Nearest city with pop. 50,000: Cape Coral, FL (35.5 miles , pop. 102,286). Najbliższe miasto z popem. 1,000,000: Houston, TX (866.0 miles , pop. 1,953,631). Single-family new house construction building permits: 1997: 70 buildings , average cost: 618,000 1998: 101 buildings , average cost: 565,800 1999: 117 buildings , average cost: 863,400 2000: 131 buildings , average cost: 837,200 2001: 122 buildings , average cost: 868,200 2002: 118 buildings , average cost: 912,700 2003: 128 buildings , average cost: 819,800 2004: 173 buildings , average cost: 912,200 2005: 192 buildings , average cost: 1,457,100 2006: 96 buildings , average cost: 1,144,000 2007: 82 buildings , average cost: 1,225,000 2008: 83 buildings , average cost: 1,536,600 2009: 39 buildings , average cost: 1,864,700 2017: 63 buildings , average cost: 1,257,500 2017: 81 buildings , average cost: 1,344,400 2017: 111 buildings , average cost: 1,715,700 2017: 146 buildings , average cost: 1,314,300 2017: 185 buildings , average cost: 1,474,100 Number of permits per 10,000 residents Management occupations (25) Sales and related occupations (20) Construction and extraction occupation s (8) Health diagnosing and treating practitioners and other technical occupations (7) Business and financial operations occupations (6) Production occupations (4) Food preparation and serving related occupations (4) Sales and related occupations (26) Office and administrative support occupations (17) Management occupations (14) Personal care and service occupations (8) Health diagnosing and treating practitioners and other technical occupations (7) Education, training, and library occupations (6) Food preparation and serving related occupations (5) Average climate in Naples, Florida Based on data reported by over 4,000 weather stations Tornado activity: Naples-area historical tornado activity is significantly below Florida state average. It is 54 smaller than the overall U. S. average. On 1191968 , a category F2 ( max. wind speeds 113-157 mph) tornado 1.2 miles away from the Naples city center killed 2 people and injured 17 people and caused between 5000 and 50,000 in damages. On 6101962 , a category F2 tornado 17.2 miles away from the city center caused between 5000 and 50,000 in damages. Earthquake activity: Naples-area historical earthquake activity is significantly below Florida state average. It is 99 smaller than the overall U. S. average. On 9102006 at 14:56:08 , a magnitude 5.9 (5.9 MB , 5.5 MS , 5.8 MW , Depth: 8.7 mi , Class: Moderate , Intensity: VI - VII) earthquake occurred 299.9 miles away from the city center On 3311992 at 14:59:39 , a magnitude 3.8 (3.8 MB , Depth: 3.1 mi , Class: Light , Intensity: II - III) earthquake occurred 244.5 miles away from Naples center On 4181997 at 14:57:35 , a magnitude 3.9 (3.9 MB , Depth: 20.5 mi) earthquake occurred 296.7 miles away from the city center On 2221992 at 04:21:34 , a magnitude 3.2 (3.2 MB , Depth: 6.2 mi) earthquake occurred 181.1 miles away from the city center On 2102006 at 04:14:22 , a magnitude 5.3 (4.2 MB , 5.3 MS , Depth: 3.1 mi) earthquake occurred 531.1 miles away from Naples center On 4132003 at 04:52:53 , a magnitude 3.2 (3.2 MB , Depth: 6.2 mi) earthquake occurred 266.2 miles away from the city center Magnitude types: body-wave magnitude (MB), surface-wave magnitude (MS), moment magnitude (MW) Natural disasters: The number of natural disasters in Collier County (26) is a lot greater than the US average (13). Major Disasters (Presidential) Declared: 16 Emergencies Declared: 5 Causes of natural disasters: Hurricanes: 11 , Fires: 7 , Tropical Storms: 5 , Floods: 2 , Freezes: 2 , Tornadoes: 2 , Heavy Rain: 1 , Wind: 1 (Note: Some incidents may be assigned to more than one category). Birthplace of: Chris Resop - 2005 Major League Baseball player (Florida Marlins, born . Nov 4, 1982) , Cleannord Saintil - Football player , Crafton Wallace - Mixed martial artist , Earnest Graham - 2005 NFL player (Tampa Bay Buccaneers, born . Jan 15, 1980) , Fred McCrary - 2005 NFL player (Atlanta Falcons, born . Sep 19, 1972) , George McNeill - Professional golfer , Jesse Witten - Tennis player , Spencer Adkins - Football player , Tina Wainscott - Writer , Chris Johnson (baseball) - Baseball player. Main business address for: BANCSHARES OF FLORIDA INC ( NATIONAL COMMERCIAL BANKS ), SUMMIT AMERICA TELEVISION INC TN ( RETAIL-CATALOG MAIL-ORDER HOUSES ), BEASLEY BROADCAST GROUP INC ( RADIO BROADCASTING STATIONS ), FIRST NATIONAL BANKSHARES OF FLORIDA INC ( STATE COMMERCIAL BANKS ), TIB FINANCIAL CORP. ( STATE COMMERCIAL BANKS ), HEALTH MANAGEMENT ASSOCIATES INC ( SERVICES-GENERAL MEDICAL SURGICAL HOSPITALS, NEC ). Hospitals in Naples: AVOW HOSPICE INC (1095 WHIPPOORWILL LANE) DOCTORS OUTPATIENT SURGERY CENTER, LLC (1005 CROSSPOINTE DRIVE, SUITE 2) NAPLES COMMUNITY HOSPITAL (Voluntary non-profit - Private, 350 7TH ST N) PHYSICIANS REGIONAL MEDICAL CENTER - PINE RIDGE (Proprietary, provides emergency services, 6101 PINE RIDGE ROAD) WILLOUGH AT NAPLES, THE (9001 TAMIAMI TRAIL EAST) Nursing Homes in Naples: ARISTOCRAT, THE (10949 PARNU STREET) BENTLEY CARE CENTER (875 RETREAT DRIVE) CHATEAU AT MOORINGS PARK, THE (130 MOORINGS PARK DRIVE) HARBORCHASE OF NAPLES (7801 AIRPORT PULLING ROAD N) HERITAGE HEALTH CARE CENTER (777 9TH ST) HERITAGE HEALTHCARE AND REHABILITATION CENTER (777 9TH ST N) IMPERIAL HEALTH CARE CENTER (900 IMPERIAL GOLF COURSE BLVD) LAKESIDE PAVILLION CARE AND REHABILITATION CENTER (2900 12TH STREET N) MANORCARE AT LELY PALMS (6135 RATTLESNAKE HAMMOCK ROAD) MANORCARE NURSING AND REHABILITATION CENTER (3601 LAKEWOOD BLVD) PREMIER PLACE AT THE GLENVIEW (100 GLENVIEW PLACE) Dialysis Facil ities in Naples: ARA - NAPLES DIALYSIS CENTER LLC (4529 EXECUTIVE DRIVE) ARA - NAPLES SOUTH DIALYSIS CENTER LLC (4270 TAMIAMI TRAIL EAST SUITE 1) BMA - SOUTH COLLIER (12703 TAMIAMI TRAIL EAST 121) KIDNEY INSTITUTE OF NAPLES (878 109TH AVE N SUITE 1) NAPLES ARTIFICIAL KIDNEY CENTER (3699 AIRPORT PULLING RD N) NORTH NAPLES DIALYSIS LLC (1750 SW HEALTH PKWY) NRI - NAPLES (6625 HILLWAY CIRCLE) Home Health Centers in Naples: AMERICARE HOME HEALTH SERVICES, INC (5020 TAMIAMI TRL N SUITE 200) GENTIVA HEALTH SERVICES (5050 TAMIAMI TRL N UNIT B) MOORINGS PARK HOME HEALTH AGENCY (111 MOORINGS PARK DR) UNS UNITED NURSING SERVICES (5644 TAVILLA CIR SUITE 204) WEST COAST HOME HEALTH CARE AGENCY INC (2590 NORTHBROOKE PLAZA DR UNIT 203) XL - CARE AGENCY INC OF COLLIER (2640 GOLDEN GATE PARKWAY SUITE 206) Airports and heliports located in Naples: Amtrak station: NAPLES (I-75 AT RTE. 951) - Bus Station . Services: enclosed waiting area. CollegesUniversities in Naples: Hodges University ( Full-time enrollment: 2,132 Location: 2655 Northbrooke Drive Private, not-for-profit Website: hodges. edu Offers Masters degree ) Lorenzo Walker Institute of Technology ( FT enrollment: 539 Location: 3702 Estey Ave Public Website: lwit. edu) Wolford College ( FT enrollment: 250 Location: 1336 Creekside Boulevard, Suite 2 Private, for-profit Website: wolford. edu Offers Doctors degree ) Ave Maria School of Law ( Location: 1025 Commons Circle Private, not-for-profit Website: avemarialaw. edu Offers Doctors degree ) Other collegesuniversities with over 2000 students near Naples: Florida Gulf Coast University ( about 22 miles Fort Myers, FL Full-time enrollment: 11,165) Edison State College ( about 29 miles Fort Myers, FL FT enrollment: 10,649) DeVry University-Florida ( about 92 miles Miramar, FL FT enrollment: 3,674) Florida International University ( about 93 miles Miami, FL FT enrollment: 41,234) Florida Career College-Miami ( about 9 4 miles Miami, FL FT enrollment: 10,133) Florida National University-Main Campus ( about 94 miles Hialeah, FL FT enrollment: 4,106) Nova Southeastern University ( about 97 miles Fort Lauderdale, FL FT enrollment: 25,621) Biggest public high schools in Naples: Private high schools in Naples: THE COMMUNITY SCHOOL OF NAPLES ( Students: 726, Location: 13275 LIVINGSTON RD, Grades: PK-12) SEACREST COUNTRY DAY SCHOOL ( Students: 508, Location: 7100 DAVIS BLVD, Grades: PK-12) FIRST BAPTIST ACADEMY ( Students: 506, Location: 3000 ORANGE BLOSSOM DR, Grades: PK-12) ST JOHN NEUMANN CATHOLIC HIGH SCHOOL ( Students: 216, Location: 3000 53RD ST SW, Grades: 9-12) NICAEA ACADEMY ( Students: 193, Location: 14785 COLLIER BLVD, Grades: PK-12) ADONAI ACADEMY ( Students: 59, Location: 2590 NORTHBROOKE PLAZA DR STE 205, Grades: KG-12) INTERNATIONAL LEARNING ACADEMY ( Students: 56, Location: 2248 AIRPORT RD S, Grades: UG-12) CORKSCREW CHRISTIAN SCHOOL ( Students: 14, Location: 22022 IMMOKALEE RD, Grades: P K-12) Biggest public elementarymiddle schools in Naples: Biggest private elementarymiddle schools in Naples: THE VILLAGE SCHOOL ( Students: 488, Location: 6000 GOODLETTE RD N, Grades: PK-8) ST ANN SCHOOL ( Students: 310, Location: 542 8TH AVE S, Grades: PK-8) ST ELIZABETH SETON SCHOOL ( Students: 256, Location: 2730 53RD TER SW, Grades: PK-8) ROYAL PALM ACADEMY ( Students: 245, Location: 16100 LIVINGSTON RD, Grades: PK-8) NAPLES CHRISTIAN ACADEMY ( Students: 142, Location: 3161 SANTA BARBARA BLVD, Grades: PK-8) MONTESSORI ACADEMY OF NAPLES ( Students: 91, Location: 2659 PROFESSIONAL CIR STE 1118, Grades: UG-5) NAPLES ADVENTIST CHRISTIAN SCHOOL ( Students: 63, Location: 2629 HORSESHOE DR S, Grades: PK-8) ABLE ACADEMY ( Students: 40, Location: 5860 GOLDEN GATE PKWY, Grades: PK-6) GRACE COMMUNITY DAYCARE SCHOOL ( Students: 30, Location: 5524 19TH CT SW, Grades: PK-4) WAVES OF WONDER MONTESSORI SCHOOL ( Students: 29, Location: 7740 PRESERVE LN STE 1, Grades: PK-3) Library in Naples: COLLI ER COUNTY PUBLIC LIBRARY ( Operating income: 9,409,013 Location: 2385 ORANGE BLOSSOM DRIVE 533,096 books 27,441 e-books 34,433 audio materials 51,567 video materials 18 local licensed databases 62 state licensed databases 867 print serial subscriptions ) User submitted facts and corrections: for the hospitals listed in naples, you should change the cleveland clinic to its new name of Physicians Regional Medical Center Public high schools in Naples: Golden Gate High School needs to be added to the list Add Palmetto Ridge High School to Naples, Florida Notable locations in Naples: Kokomis Ferry (A). Miccosukee Golf and Country Club (B). City of Naples Wastewater Treatment Facility (C). Naples Depot Cultural Center (D). Collier County Public Library Naples Branch (E). North Naples Fire Control and Rescue District Station 47 (F). Collier County Emergency Medical Services Station 24 (G). Collier County Emergency Medical Services Station 2 (H). Collier County Emergency Medical Services Helicopter Operations Center (I). Collier County Emergency Medical Services Station 1 (J). City of Naples Fire Department Station 2 (K). City of Naples Fire Department Station 3 (L). City of Naples Fire Department Station 1 (M). East Naples Fire Control and Rescue District Station 24 (N). Naples Police Department (O). Federal Bureau of Investigation (P). Displayhide their locations on the map Main business address in Naples include: BANCSHARES OF FLORIDA INC (A). SUMMIT AMERICA TELEVISION INC TN (B). BEASLEY BROADCAST GROUP INC (C). FIRST NATIONAL BANKSHARES OF FLORIDA INC (D). TIB FINANCIAL CORP. (E). Displayhide their locations on the map Churches in Naples include: Jehovahs Witness Spanish Congregation Church (A). The Salvation Army Church (B). Unitarian Universalist Congregation Church (C). Episcopal Trinity By-the-Cove Church (D). Baptist Church of Estero (E). Catholic Church Catholic Sisters Guadalupanas (F). Charisma Chapel (G). Church of Christ (H). Church of God in Naples (I). Displayhide their locations on the map Tourist attractions: Conservancy of Southwest Florida (Museums 1450 Merrihue Drive) (1). Collier County Museum (3301 Tamiami Trail East Building J) (2). Kelseys Collection - LLC (Art Museums 567 Park Street) (3). Aviary Zoo of Naples (Cultural Attractions - Events - Facilities 9824 Immokalee Road) (4). Holocaust Museum of Southwest Florida (Cultural Attractions - Events - Facilities 4760 Tamiami Trail North Suite 7) (5). Bird Gardens (Cultural Attractions - Events - Facilities 1060 Purple Martin Drive) (6). Educational Services (Cultural Attractions - Events - Facilities 9824 Immokalee Road) (7). E Group Inc (Cultural Attractions - Events - Facilities 9824 Immokalee Road) (8). Collier County Historical Society (Cultural Attractions - Events - Facilities 137 12th Avenue South) (9). Displayhide their approximate locations on the map Hotels: Chalet Apartment Motel Condos (844 Wiggins Passage Road West) (1). Broadwells Restaurant (851 Gulf Shore Boulevard North) (2). Best Western Naples Inn (2329 9th Street North) (3). Chickee Hut (11000 Gulf Shore Drive) (4). Baymont Inn Suites (185 Bedzel Circle) (5). Best Western Naples Plaza Hotel (6400 Dudley Drive) (6). Bellasera (221 Ninth Street South) (7). Charter Club Resort of Naples Bay (1000 10th Avenue South) (8). Baymont Inn Naples (185 Bedzel Circle) (9). Displayhide their approximate locations on the map Courts: Paladin Financial Court (1767 Knights) (1). Florida State - Judicial - Circuit Court Twentieth Judicial - Clerk Of Court Off (4715 Golden Gate Parkway) (2). Collier County of CONT - Clerk of the Circuit Court Satellite Office - Greentree Shopping Ce (2376 Immokalee Road) (3). Displayhide their approximate locations on the map Collier County has a predicted average indoor radon screening level less than 2 pCiL (pico curies per liter) - Low Potential Air pollution and air quality trends (lower is better) Air Quality Index (AQI) level in 2017 was 45.0 . This is significantly better than average. Likely homosexual households (counted as self-reported same-sex unmarried-partner households) Lesbian couples: 0.3 of all households Gay men: 0.3 of all households People in group quarters in Naples in 2017: 261 people in nursing facilitiesskilled-nursing facilities 11 people in workers group living quarters and job corps centers 7 people in hospitals with patients who have no usual home elsewhere 267 people in nursing homes in 2000 4 people in religious group quarters in 2000 Banks with most branches in Naples (2017 data): Fifth Third Bank: 18 branches . Info updated 20091005: Bank assets: 114,540.4 mil , Deposits: 89,689.1 mil , headquarters in Cincinnati, OH , positive income . Commercial Lending Specialization , 1378 total offices , Holding Company: Fifth Third Bancorp Bank of America, National Association: 15 branches . Info updated 20091118: Bank assets: 1,451,969.3 mil , Deposits: 1,077,176.8 mil , headquarters in Charlotte, NC , positive income , 5782 total offices , Holding Company: Bank Of America Corporation Wells Fargo Bank, National Association: 15 branches . Info updated 20170405: Bank assets: 1,161,490.0 mil , Deposits: 905,653.0 mil , headquarters in Sioux Falls, SD , positive income , 6395 total offices , Holding Company: Wells Fargo Company Regions Bank: 13 branches . Info updated 20170224: Bank assets: 123,368.2 mil , Deposits: 98,301.3 mil , headquarters in Birmingham, AL , positive income . Commercial Lending Specialization , 1778 total offices , Holding Company: Regions Financial Corporation SunTrust Bank: 8 branches . Info updated 20170527: Bank assets: 171,291.7 mil , Deposits: 129,833.2 mil , headquarters in Atlanta, GA , positive income . Commercial Lending Specialization , 1716 total offices , Holding Company: Suntrust Banks, Inc. JPMorgan Chase Bank, National Association: Naples Branch, Aston Gardens Naples Banking Center, Naples Office, Radio Road Santa Barbara Blvd Bank, Us 41 And Rattlesnake Hammock Road B, Airport Pulling Pine Ridge Banking . Zaktualizowano informację 20171110: Aktywa bankowe: 1 811 678,0 mln, Depozyty: 1 190 738 mln, siedziba główna w Columbus, OH, dodatnie dochody. International Specialization , 5577 total offices , Holding Company: Jpmorgan Chase Co. Branch Banking and Trust Company: North Naples Branch, Pine Ridge Branch, Downtown Naples Branch, Pebblebrooke Branch, Davis Boulevard Branch, Naples Branch . Info updated 20170329: Bank assets: 168,867.6 mil , Deposits: 127,549.5 mil , headquarters in Winston Salem, NC , positive income . Commercial Lending Specialization , 1793 total offices , Holding Company: BbT Corporation PNC Bank, National Association: Naples Newgate Center Branch, National City Pcg Branch, Galleria Court Branch, 5th Avenue Naples Branch, Radio Road Branch, North Naples Branch . Info updated 20170320: Bank assets: 263,309.6 mil , Deposits: 197,343.0 mil , headquarters in Wilmington, DE , positive income . Commercial Lending Specialization , 3085 total offices , Holding Company: Pnc Financial Services Group, Inc. The Iberiabank: North Naples Branch, Pine Ridge Road Branch, Downtown Naples Branch, Park Shore Branch, Airport Road Branch, Orion Bank . Info updated 20170608: Bank assets: 11,676.7 mil , Deposits: 9,387.9 mil , headquarters in Lafayette, LA , positive income . Commercial Lending Specialization , 187 total offices , Holding Company: Iberiabank Corporation 30 other banks with 50 local branches Educational Attainment () in 2018 Naples government finances - Expenditure in 2002 (per resident): Construction - Air Transportation: 8,361,000 (398.75) Sewerage: 3,890,000 (185.52) Water Utilities: 3,890,000 (185.52) Protective Inspection Regulation, NEC: 1,588,000 (75.73) Parks Recreation: 1,445,000 (68.91) Regular Highways: 932,000 (44.45) Police Protection: 510,000 (24.32) Housing Community Development: 185,000 (8.82) Financial Administration: 130,000 (6.20) Fire Protection: 99,000 (4.72) Current Operations - Police Protection: 6,536,000 (311.71) Air Transportation: 5,637,000 (268.84) Sewerage: 4,887,000 (233.07) Solid Waste Management: 4,573,000 (218.09) Water Utilities: 4,155,000 (198.16) Fire Protection: 3,548,000 (169.21) Parks Recreation: 3,174,000 (151.37) Regular Highways: 2,149,000 (102.49) Protective Inspection and Regulation, NEC: 1,477 ,000 (70.44) Central Staff Services: 1,379,000 (65.77) Parking Facilities: 1,178,000 (56.18) Sea and Inland Port Facilities: 1,012,000 (48.26) Financial Administration: 912,000 (43.49) Judicial and Legal Services: 434,000 (20.70) Housing Community Development: 36,000 (1.72) General - Interest on Debt: 1,725,000 (82.27) Total Salaries Wages: 18,613,000 (887.69) Water Utilities - Interest on Debt: 1,361,000 (64.91) Naples government finances - Revenue in 2002 (per resident): Charges - Air Transportation: 8,498,000 (405.28) Charges - Sewerage: 8,890,000 (423.98) Solid Waste Management: 4,725,000 (225.34) Parks Recreation: 1,430,000 (68.20) All Other: 1,387,000 (66.15) Sea and Inland Port Facilities: 1,369,000 (65.29) Parking Facilities: 413,000 (19.70) Federal Intergovernmental - All Other: 473,000 (22.56) Local Intergovernmental - All Other: 1,338,000 (63.81) Miscellaneous - Interest Earnings: 3,349,000 (159.72) General Revenue, NEC: 701,000 (33.43) Special Assessments: 540,000 (25.75 ) Revenue - Water Utilities: 9,413,000 (448.92) State Intergovernmental - General Support: 3,491,000 (166.49) All Other: 132,000 (6.30) Tax - Property: 8,718,000 (415.78) Public Utilities: 5,614,000 (267.74) Other Selective Sales: 2,823,000 (134.63) NEC: 2,130,000 (101.58) Motor Fuels Sales: 1,846,000 (88.04) Naples government finances - Debt in 2002 (per resident): Long Term Debt Beginning Outstanding - Water Utilities: 22,685,000 (1081.89) Long Term Debt Beginning Outstanding, NEC: 9,260,000 (441.63) Long Term Debt Issue, Unspecified - Water Utilities: 7,275,000 (346.96) Other NEC: 3,205,000 (152.85) Long Term Debt Outstanding - Full Faith Credit - Other, NEC: 8,270,000 (394.41) Long Term Debt Outstanding Nonguaranteed - Water Utilities: 20,545,000 (979.83) Other, NEC: 3,207,000 (152.95) Long Term Debt Retired Unspecified - Water Utilities: 9,415,000 (449.02) Other, NEC: 988,000 (47.12) Short Term Debt Outstanding - End of Fiscal Year: 71,878,000 (3427.99) Beginning: 67,299,000 (320 9.61) Naples government finances - Cash and Securities in 2002 (per resident): Bond Fund - Cash Deposits: 8,136,000 (388.02) Other Funds - Cash Deposits: 35,806,000 (1707.65) Sinking Fund - Cash Deposits: 1,565,000 (74.64) 7.35 of this countys 2017 resident taxpayers lived in other counties in 2017 (104,488 average adjusted gross income ) Strongest AM radio stations in Naples: WNOG (1270 AM 5 kW NAPLES, FL Owner: MERIDIAN BROADCASTING, INC.) WVOI (1480 AM 10 kW MARCO ISLAND, FL Owner: ALL FINANCIAL NETWORK, INC.) WCNZ (1660 AM 10 kW MARCO ISLAND, FL Owner: ALL FINANCIAL NETWORK, INC.) WJNA (640 AM 38 kW ROYAL PALM BEACH, FL Owner: SOUTH FLORIDA RADIO, INC.) WWFE (670 AM 50 kW MIAMI, FL Owner: FENIX BROADCASTING CORP.) WAQI (710 AM 50 kW MIAMI, FL Owner: LICENSE CORPORATION 1) WVCG (1080 AM 50 kW CORAL GABLES, FL Owner: RADIO ONE LICENSES, LLC) WWCN (770 AM 10 kW NORTH FORT MYERS, FL Owner: WJPT LICENSE LIMITED PARTNERSHIP) WQBA (1140 AM 50 kW MIAMI, FL Owner: WQBA-AM LICENSE CORP.) WRFX (940 AM 50 kW MIAMI, FL Owner: CLEAR CHANNEL BROADCASTING LICENSES, INC.) WSUA (1260 AM 50 kW MIAMI, FL Owner: WSUA BROADCASTING CORPORATION) WNMA (1210 AM 49 kW MIAMI SPRINGS, FL Owner: RADIO UNICA OF MIAMI LICENSE CORP.) WPTK (1200 AM 10 kW PINE ISLAND CENTER, FL Owner: FORT MYERS BROADCASTING COMPANY) Strongest FM radio stations in Naples: WTLT (93.7 FM NAPLES, FL Owner: MERIDIAN BROADCASTING, INC.) WRXK-FM (96.1 FM BONITA SPRINGS, FL Owner: WRXK LICENSE LIMITED PARTNERSHIP) WARO (94.5 FM NAPLES, FL Owner: MERIDIAN BROADCASTING, INC.) WAVV (101.1 FM MARCO, FL Owner: ALPINE BROADCASTING CORP. INC.) WBTT (105.5 FM NAPLES PARK, FL Owner: CLEAR CHANNEL BROADCASTING LICENSES, INC.) WDRR (107.1 FM LEHIGH ACRES, FL Owner: CLEAR CHANNEL BROADCASTING LICENSES, INC.) WSRX (89.5 FM NAPLES, FL Owner: SHADOWLAWN ASSOCIATION, INC.) WSOR (90.9 FM NAPLES, FL Owner: THE MOODY BIBLE INSTITUTE OF CHICAGO) WWGR (101.9 FM FORT MYERS, FL Owner: RENDA BROADCASTING CORP. OF NEVADA) WGUF (98.9 FM MARCO , FL Owner: RENDA BROADCASTING CORP. OF NEVADA) WSGL (104.7 FM NAPLES, FL Owner: RENDA BROADCASTING CORPORATION OF NEVADA) WAYJ (88.7 FM FORT MYERS, FL Owner: WAY-FM MEDIA GROUP. INC.) WINK-FM (96.9 FM FORT MYERS, FL Owner: FORT MYERS BROADCASTING COMPANY) WXKB (103.9 FM CAPE CORAL, FL Owner: WXKB LICENSE LIMITED PARTNERSHIP) WMKO (91.7 FM MARCO, FL Owner: BOARD OF TRUSTEES, FLORIDA GULF COAST UNIVERSITY) WNRW (98.5 FM SAN CARLOS PARK, FL Owner: BEL MEADE BROADCASTING COMPANY, INC.) WJBX (99.3 FM FORT MYERS BEACH, FL Owner: WJBX LICENSE LIMITED PARTNERSHIP) WJPT (106.3 FM FORT MYERS, FL Owner: WJPT LICENSE LIMITED PARTNERSHIP) WCKT (100.1 FM PORT CHARLOTTE, FL Owner: CLEAR CHANNEL BROADCASTING LICENSES, INC.) WTLQ-FM (97.7 FM PUNTA RASSA, FL Owner: FORT MYERS BROADCASTING COMPANY) TV broadcast stations around Naples: W56DW ( Channel 56 NAPLES, FL Owner: TRINITY BROADCASTING NETWORK) WWDT-CA ( Channel 43 NAPLES, FL Owner: RUSSELL R. WEDDELL) WXDT-LP ( Channel 23 NAPLES, FL Owner: GUENTER MARKSTEINER) WYDT-CA ( Channel 32 NAPLES, FL Owner: GUENTER MARKSTEINER) WZDT-LP ( Channel 39 NAPLES, FL Owner: GUENTER MARKSTEINER) WTIG-LP ( Channel 2 NAPLES, FL Owner: TIGER EYE BROADCASTING CORPORATION) WZVN-TV ( Channel 26 NAPLES, FL Owner: MONTCLAIR COMMUNICATIONS, INC.) WINK-TV ( Channel 11 FORT MYERS, FL Owner: FORT MYERS BROADCASTING COMPANY) WTVK ( Channel 46 NAPLES, FL Owner: ACME TELEVISION LICENSES OF FLORIDA, LLC) WFTX ( Channel 36 CAPE CORAL, FL Owner: EMMIS TELEVISION LICENSE CORPORATION) WRXY-TV ( Channel 49 TICE, FL Owner: WEST COAST CHRISTIAN TELEVISION, INC) WBBH-TV ( Channel 20 FORT MYERS, FL Owner: WATERMAN BROADCASTING CORP. OF FLORIDA) WBSP-CA ( Channel 9 NAPLES, FL Owner: CALOOSA TELEVISION CORPORATION) W22CL ( Channel 22 FORT MYERS, FL Owner: ARKANSAS MEDIA, LLC) WDPX-LP ( Channel 18 FORT MYERS, FL Owner: TIGER EYE BROADCASTING CORP.) Fatal accident count (per 100,000 population) Drinking water stations with addresses in Naples and their reported violations in the past: GOODLAND WATER COMPANY ( Population served: 770 , Purch surface water): Past monitoring violations: Monthly Turbidity Exceed (Enhanced SWTR) - In SEP-2006 , Contamina nt: IESWTR . Follow-up actions: St Public Notif requested (SEP-25-2006), St Public Notif received (SEP-25-2006) Monitoring, Turbidity (Enhanced SWTR) - In SEP-2006 , Contaminant: IESWTR . Follow-up actions: St Public Notif requested (SEP-25-2006), St Public Notif received (SEP-25-2006) IGLESIA GETSEMANI CHURCH ( Population served: 78 , Groundwater): Past health violations: MCL, Monthly (TCR) - In AUG-2017 , Contaminant: Coliform . Follow-up actions: St Public Notif requested (AUG-31-2017) , St Public Notif received (AUG-31-2017) TEMPLE BETHEL ( Population served: 40 , Groundwater): Past health violations: MCL, Monthly (TCR) - In MAY-2017 , Contaminant: Coliform . Follow-up actions: St Compliance achieved (JUN-05-2017) Past monitoring violations: Failure to Conduct Assessment Monitoring - Between JUL-2017 and SEP-2017 , Contaminant: E. COLI Failure to Conduct Assessment Monitoring - Between JAN-2017 and MAR-2017 , Contaminant: E. COLI . Follow-up actions: St Compliance achieved (MAY-01-2017), St Public Notif requested (MAY-04-2017) Failure to Conduct Assessment Monitoring - Between JUL-2017 and SEP-2017 , Contaminant: E. COLI . Follow-up actions: St Public Notif requested (OCT-27-2017), St Compliance achieved (DEC-20-2017) 4 routine major monitoring violations One regular monitoring violation NAPLES EQUESTRIAN CHALLENGE, INC. ( Population served: 30 , Groundwater): Past monitoring violations: One routine major monitoring violation One regular monitoring violation Drinking water stations with addresses in Naples that have no violations reported: COLLIER COUNTY REGIONAL WTP ( Population served: 134,780 , Primary Water Source Type: Groundwater) LIVING WORD FAMILY CHURCH WTP ( Population served: 500 , Primary Water Source Type: Groundwater) AURORA ACRES ( Population served: 170 , Primary Water Source Type: Groundwater) HIDEOUT GOLF CLUB SYSTEM ( Population served: 100 , Primary Water Source Type: Groundwater) STAR QUICK MART ( Population served: 60 , Primary Water Source Type: Groundwater) RANDALL CENTER ( Population served: 50 , Primary Water Source Type: Groundwater) SYNGENTA SEEDS, INC. ( Population served: 28 , Primary Water Source Type: Groundwater) NAPLES BINGO PALACE GG PKWY ( Population served: 25 , Primary Water Source Type: Groundwater) UNITY FAITH MISSIONARY BAPTIST ( Population served: 25 , Primary Water Source Type: Groundwater) 2006 National Fire Incident Reporting System Incidents: Incident types - Naples Fire-safe hotels and motels in Naples, Florida: Whites Motel, 11238 E Tamiami TRL, Naples, Florida 33962 Ramada Inn Of Naples, 1100 Tamiami Trail N, Naples, Florida 34102 . Phone: (239) 263-3434, Fax: (239) 262-7439 The Naples Beach Hotel Golf Club, 851 Gulfshore Blvd N, Naples, Florida 34102 . Phone: (239) 261-2222, Fax: (239) 435-4360 Sea Shell Motel, 82 S 9TH St, Naples, Florida 33940 Glades Motel, 3115 E Tamiami TRL, Naples, Florida 33962 Tiki Motel Apartments, 2486 Tamiami TRL E, Naples, Florida 33962 Gulfstream Motel, 4520 Gulf STRM Dr, Naples, Florida 33962 Best Western Naples Plaza, 6400 Dudley Dr, Naples, Florida 34105 . Phone: (239) 643-6655, Fax: (239) 643-4063 21 other hotels and motels All 29 fire-safe hotels and motels in Naples, FloridaMost common first names in Naples, FL among deceased individuals Naples compared to Florida state average: Median household income above state average. Median house value significantly above state average. Odsetek bezrobotnych znacznie poniżej średniej państwowej. Procent populacji czarnej rasy znacznie poniżej średniej krajowej. Hispanic race population percentage significantly below state average. Median age significantly above state average. Procent populacji urodzony zagranicą poniżej średniej krajowej. Renting percentage below state average. Number of college students below state average. Procent ludności posiadającej stopień licencjata lub wyższy znacznie powyżej średniej krajowej. Naples on our top lists : 6 on the list of Top 101 cities with largest percentage of females in industries: Real estate and rental and leasing (population 5,000) 7 on the list of Top 101 cities with the highest cost per building permit(population 5,000) 24 on the list of Top 101 cities with the most local government spending on current operations of parking facilities per resident (population 10,000) 25 on the list of Top 101 cities with the highest percentage of workers working at home, population 5,000 27 on the list of Top 101 cities with largest percentage of females in occupations: Sales and related occupations (population 5,000) 32 on the list of Top 100 cities with oldest residents (pop. 5,000) 34 on the list of Top 101 cities with largest percentage of males in occupations: Management occupations (population 5,000) 42 on the list of Top 101 cities that people commute into (largest positive percentage daily daytime population change due to commuting) (population 5,000) 61 on the list of Top 101 cities with the most people born in other U. S. states (population 5,000) 62 on the list of Top 101 cities with largest percentage of males in industries: Real estate and rental and leasing (population 5,000) 67 on the list of Top 100 cities with highest ratio of median house value to median household income (pop. 5,000) 69 on the list of Top 101 cities with the most full-time park and recreation workers per 1000 residents (population 5,000) 70 on the list of Top 101 cities with the most full-time firefighters per 1000 residents (population 5,000) 73 on the list of Top 101 cities with the most full-time financial administration workers per 1000 residents (population 5,000) 12 (34102) on the list of Top 101 zip codes with the highest 2017 average taxable interest for individuals (pop 5,000) 17 (34102) on the list of Top 101 zip codes with the highest 2017 average net capital gainloss (pop 5,000) 18 (34102) on the list of Top 101 zip codes with the highest 2017 average Adjusted Gross Income (AGI) for individuals (pop 5,000) 34 (34102) on the list of Top 101 zip codes with the largest charity contributions deductions as a percentage of AGI in 2017 (pop 5,000) 42 (34103) on the list of Top 101 zip codes with the smallest percentage of returns reporting salary or wage in 2017 (pop 5,000) 65 (34103) o n the list of Top 101 zip codes with the most beauty salons in 2005 83 (34102) on the list of Top 101 zip codes with the highest average reported salarywage in 2017 (pop 5,000) 84 (34102) on the list of Top 101 zip codes with the most offices of physicians in 2005 1 on the list of Top 101 counties with the largest number of people without health insurance coverage in 2000 (pop. 50,000) 18 on the list of Top 101 counties with the largest decrease in the number of infant deaths per 1000 residents 2000-2006 to 2007-2017 (pop. 50,000) 23 on the list of Top 101 counties with the lowest number of infant deaths per 1000 residents 2007-2017 (pop. 50,000) 25 on the list of Top 101 counties with the largest decrease in the number of births per 1000 residents 2000-2006 to 2007-2017 (pop 50,000) 50 on the list of Top 101 counties with the highest ground withdrawal of fresh water for public supply There are 865 pilots and 408 other airmen in this city. Top Patent Applicants Peter J. Dreyfuss (47) Reinhold Schmieding (35) Ricardo Albertorio (22) Jeffrey Wyman (22) Thomas Dooney, Jr. (21) Jacob A. Jolly (18) Philip B. Harris (16) Scott K. Mitchell (16) Arthrex, Inc. (16) Brandon L. Roller (14) Total of 1099 patent applications in 2008-2017. Ostatnie sprzedaże domów, trendy cenowe i ewaluacja wartości do domu obsługiwane przez Onboard Informatics copy 2017 Onboard Informatics. Informacja jest uznawana za rzetelną, ale nie jest gwarantowana. Dane miejskie nie gwarantują dokładności ani aktualności jakichkolwiek informacji na tej stronie. Używaj na własne ryzyko. Kopia strony 2017 Advameg, Inc.
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