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:'' "Energy has to do with possibilities. Entropy has to do with the probabilities of those possibilities happening. It takes energy and performs a further epistemological step." '' '''Constantino Tsallis''' <ref>http://www.mlahanas.de/Greeks/new/Tsallis.htm</ref> | :'' "Energy has to do with possibilities. Entropy has to do with the probabilities of those possibilities happening. It takes energy and performs a further epistemological step." '' | ||
'''Entropy''' was first described by [[Rudolf Julius Emanuel Clausius]] in 1865 <ref>[http://dx.doi.org/10.1002/andp.18652010702 R. Clausius "Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie", Annalen der Physik und Chemie '''125''' pp. 353-400 (1865)]</ref>. The [[statistical mechanics | statistical mechanical]] desciption is due to [[Ludwig Eduard Boltzmann]] (Ref. ?) | ::::: '''[[Constantino Tsallis]]''' <ref>http://www.mlahanas.de/Greeks/new/Tsallis.htm</ref> | ||
'''Entropy''' was first described by [[Rudolf Julius Emanuel Clausius]] in 1865 <ref>[http://dx.doi.org/10.1002/andp.18652010702 R. Clausius "Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie", Annalen der Physik und Chemie '''125''' pp. 353-400 (1865)]</ref>. The [[statistical mechanics | statistical mechanical]] desciption is due to [[Ludwig Eduard Boltzmann]] (Ref. ?). | |||
==Classical thermodynamics== | ==Classical thermodynamics== | ||
In [[classical thermodynamics]] one has the entropy, <math>S</math>, | In [[classical thermodynamics]] one has the entropy, <math>S</math>, | ||
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In [[statistical mechanics]] entropy is defined by | In [[statistical mechanics]] entropy is defined by | ||
:<math>\left. S \right. | :<math>\left. S \right. = -k_B \sum_m p_m \ln p_m</math> | ||
where <math>k_B</math> is the [[Boltzmann constant]], | where <math>k_B</math> is the [[Boltzmann constant]], ''m'' is the index for the [[microstate |microstates]], and <math>p_m</math> | ||
is the probability that microstate '' | is the probability that microstate ''m'' is occupied. | ||
In the [[microcanonical ensemble]] this gives: | In the [[microcanonical ensemble]] this gives: | ||
:<math>\left.S\right. = k_B \ln | :<math>\left.S\right. = k_B \ln \Omega</math> | ||
where <math> | where <math>\Omega</math> (sometimes written as <math>W</math>) | ||
is the number of microscopic configurations that result in the observed macroscopic description of the thermodynamic system. | is the number of microscopic configurations that result in the observed macroscopic description of the thermodynamic system. | ||
This equation provides a link between [[Classical thermodynamics | classical thermodynamics]] and | This equation provides a link between [[Classical thermodynamics | classical thermodynamics]] and | ||
[[Statistical mechanics | statistical mechanics]] | [[Statistical mechanics | statistical mechanics]] | ||
==Arrow of time== | ==Arrow of time== | ||
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*[http://dx.doi.org/10.1063/1.881363 Joel L. Lebowitz "Boltzmann's Entropy and Time's Arrow", Physics Today '''46''' pp. 32-38 (1993)] | *[http://dx.doi.org/10.1063/1.881363 Joel L. Lebowitz "Boltzmann's Entropy and Time's Arrow", Physics Today '''46''' pp. 32-38 (1993)] | ||
*[http://dx.doi.org/10.1023/A:1023715732166 Milan M. Ćirković "The Thermodynamical Arrow of Time: Reinterpreting the Boltzmann–Schuetz Argument", Foundations of Physics '''33''' pp. 467-490 (2003)] | *[http://dx.doi.org/10.1023/A:1023715732166 Milan M. Ćirković "The Thermodynamical Arrow of Time: Reinterpreting the Boltzmann–Schuetz Argument", Foundations of Physics '''33''' pp. 467-490 (2003)] | ||
Books: | Books: | ||
* Steven F. Savitt (Ed.) "Time's Arrows Today: Recent Physical and Philosophical Work on the Direction of Time", Cambridge University Press (1997) ISBN 0521599458 | * Steven F. Savitt (Ed.) "Time's Arrows Today: Recent Physical and Philosophical Work on the Direction of Time", Cambridge University Press (1997) ISBN 0521599458 | ||
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*Ya. G. Sinai, "On the Concept of Entropy of a Dynamical System," Doklady Akademii Nauk SSSR '''124''' pp. 768-771 (1959) | *Ya. G. Sinai, "On the Concept of Entropy of a Dynamical System," Doklady Akademii Nauk SSSR '''124''' pp. 768-771 (1959) | ||
*[http://dx.doi.org/10.1063/1.1670348 William G. Hoover "Entropy for Small Classical Crystals", Journal of Chemical Physics '''49''' pp. 1981-1982 (1968)] | *[http://dx.doi.org/10.1063/1.1670348 William G. Hoover "Entropy for Small Classical Crystals", Journal of Chemical Physics '''49''' pp. 1981-1982 (1968)] | ||
* Arieh Ben-Naim "Entropy Demystified: The Second Law Reduced to Plain Common Sense", World Scientific (2008) ISBN 978-9812832252 | *Arieh Ben-Naim "Entropy Demystified: The Second Law Reduced to Plain Common Sense", World Scientific (2008) ISBN 978-9812832252 | ||
* Arieh Ben-Naim "Farewell to Entropy: Statistical Thermodynamics Based on Information", World Scientific (2008) ISBN 978-981-270-707-9 | *Arieh Ben-Naim "Farewell to Entropy: Statistical Thermodynamics Based on Information", World Scientific (2008) ISBN 978-981-270-707-9 | ||
==External links== | ==External links== | ||
*[http://www.mdpi.com/journal/entropy entropy] an international and interdisciplinary Open Access journal of entropy and information studies. | *[http://www.mdpi.com/journal/entropy entropy] an international and interdisciplinary Open Access journal of entropy and information studies. |