Entropy: Difference between revisions
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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> | |||
'''Entropy''' was first described by [[Rudolf Julius Emanuel Clausius]] in 1865 ( | '''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 | In [[classical thermodynamics]] one has the entropy, <math>S</math>, | ||
:<math>{\mathrm d} S = \frac{\delta Q_{\mathrm {reversible}}} {T} </math> | :<math>{\mathrm d} S = \frac{\delta Q_{\mathrm {reversible}}} {T} </math> | ||
where <math>Q</math> is the [[heat]] and <math>T</math> is the [[temperature]]. | where <math>Q</math> is the [[heat]] and <math>T</math> is the [[temperature]]. | ||
==Statistical mechanics== | ==Statistical mechanics== | ||
In [[statistical mechanics]] | In [[statistical mechanics]] entropy is defined by | ||
:<math>\left. S \right. = -k_B \sum_m p_m \ln p_m</math> | :<math>\left. S \right. = -k_B \sum_m p_m \ln p_m</math> | ||
| Line 35: | Line 35: | ||
==See also:== | ==See also:== | ||
*[[Entropy of a glass]] | *[[Entropy of a glass]] | ||
*[[H-theorem]] | |||
*[[Non-extensive thermodynamics]] | |||
*[[Shannon entropy]] | *[[Shannon entropy]] | ||
==References== | |||
<references/> | |||
'''Related reading''' | |||
== | |||
*[http://dx.doi.org/10.1119/1.1990592 Karl K. Darrow "The Concept of Entropy", American Journal of Physics '''12''' pp. 183-196 (1944)] | *[http://dx.doi.org/10.1119/1.1990592 Karl K. Darrow "The Concept of Entropy", American Journal of Physics '''12''' pp. 183-196 (1944)] | ||
*[http://dx.doi.org/10.1119/1.1971557 E. T. Jaynes "Gibbs vs Boltzmann Entropies", American Journal of Physics '''33''' pp. 391-398 (1965)] | *[http://dx.doi.org/10.1119/1.1971557 E. T. Jaynes "Gibbs vs Boltzmann Entropies", American Journal of Physics '''33''' pp. 391-398 (1965)] | ||
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*[http://www.ucl.ac.uk/~ucesjph/reality/entropy/text.html S. F. Gull "Some Misconceptions about Entropy" in Brian Buck and Vincent A. MacAulay (Eds.) "Maximum Entropy in Action", Oxford Science Publications (1991)] | *[http://www.ucl.ac.uk/~ucesjph/reality/entropy/text.html S. F. Gull "Some Misconceptions about Entropy" in Brian Buck and Vincent A. MacAulay (Eds.) "Maximum Entropy in Action", Oxford Science Publications (1991)] | ||
*[http://dx.doi.org/10.2174/1874396X00802010007 Efstathios E. Michaelides "Entropy, Order and Disorder", The Open Thermodynamics Journal '''2''' pp. (2008)] | *[http://dx.doi.org/10.2174/1874396X00802010007 Efstathios E. Michaelides "Entropy, Order and Disorder", The Open Thermodynamics Journal '''2''' pp. (2008)] | ||
*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)] | |||
[[category: statistical mechanics]] | |||
[[category: Classical thermodynamics]] | |||
[[category:statistical mechanics]] | |||
[[Classical thermodynamics]] | |||
Revision as of 15:38, 11 November 2009
- "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 [2]. The statistical mechanical desciption is due to Ludwig Eduard Boltzmann (Ref. ?).
Classical thermodynamics
In classical thermodynamics one has the entropy, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S} ,
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathrm d} S = \frac{\delta Q_{\mathrm {reversible}}} {T} }
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Q} is the heat and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T} is the temperature.
Statistical mechanics
In statistical mechanics entropy is defined by
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left. S \right. = -k_B \sum_m p_m \ln p_m}
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k_B} is the Boltzmann constant, m is the index for the microstates, and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p_m} is the probability that microstate m is occupied. In the microcanonical ensemble this gives:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left.S\right. = k_B \ln \Omega}
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Omega} (sometimes written as Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle W} ) 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 and statistical mechanics
Arrow of time
Articles:
- T. Gold "The Arrow of Time", American Journal of Physics 30 pp. 403-410 (1962)
- Joel L. Lebowitz "Boltzmann's Entropy and Time's Arrow", Physics Today 46 pp. 32-38 (1993)
- Milan M. Ćirković "The Thermodynamical Arrow of Time: Reinterpreting the Boltzmann–Schuetz Argument", Foundations of Physics 33 pp. 467-490 (2003)
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
- Michael C. Mackey "Time's Arrow: The Origins of Thermodynamic Behavior" (1992) ISBN 0486432432
- Huw Price "Time's Arrow and Archimedes' Point New Directions for the Physics of Time" Oxford University Press (1997) ISBN 978-0-19-511798-1
See also:
References
Related reading
- Karl K. Darrow "The Concept of Entropy", American Journal of Physics 12 pp. 183-196 (1944)
- E. T. Jaynes "Gibbs vs Boltzmann Entropies", American Journal of Physics 33 pp. 391-398 (1965)
- Daniel F. Styer "Insight into entropy", American Journal of Physics 86 pp. 1090-1096 (2000)
- S. F. Gull "Some Misconceptions about Entropy" in Brian Buck and Vincent A. MacAulay (Eds.) "Maximum Entropy in Action", Oxford Science Publications (1991)
- Efstathios E. Michaelides "Entropy, Order and Disorder", The Open Thermodynamics Journal 2 pp. (2008)
- Ya. G. Sinai, "On the Concept of Entropy of a Dynamical System," Doklady Akademii Nauk SSSR 124 pp. 768-771 (1959)
- William G. Hoover "Entropy for Small Classical Crystals", Journal of Chemical Physics 49 pp. 1981-1982 (1968)