Entropy

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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 ^[1]

Entropy was first described by Rudolf Julius Emanuel Clausius in 1865 ^[2]. The statistical mechanical desciption is due to Ludwig Eduard Boltzmann (Ref. ?).

Contents 1 Classical thermodynamics 2 Statistical mechanics 3 Arrow of time 4 See also: 5 References 6 External links

[edit] Classical thermodynamics

In classical thermodynamics one has the entropy, S,

where Q is the heat and T is the temperature.

[edit] Statistical mechanics

In statistical mechanics entropy is defined by

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:

where Ω (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:

• Entropy of a glass
• H-theorem
• Non-extensive thermodynamics
• Shannon entropy

[edit] References

1. ↑ http://www.mlahanas.de/Greeks/new/Tsallis.htm
2. ↑ 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.