Entropy
- "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
Contents |
[edit] Classical thermodynamics
In classical thermodynamics one has the entropy, \(S\), \[{\mathrm d} S = \frac{\delta Q_{\mathrm {reversible}}} {T} \]
where \(Q\) is the heat and \(T\) is the temperature.
[edit] Statistical mechanics
In statistical mechanics entropy is defined by
\[\left. S \right. = -k_B \sum_m p_m \ln p_m\]
where \(k_B\) is the Boltzmann constant, m is the index for the microstates, and \(p_m\) is the probability that microstate m is occupied. In the microcanonical ensemble this gives:
\[\left.S\right. = k_B \ln \Omega\]
where \(\Omega\) (sometimes written as \(W\)) 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
[edit] 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
[edit] See also:
[edit] References
- ↑ http://www.mlahanas.de/Greeks/new/Tsallis.htm
- ↑ R. Clausius "Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie", Annalen der Physik und Chemie 125 pp. 353-400 (1865)
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)
- 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
[edit] External links
- entropy an international and interdisciplinary Open Access journal of entropy and information studies.
- Joel L. Lebowitz "Time's arrow and Boltzmann's entropy", Scholarpedia, 3(4):3448 (2008)
