Entropy

The entropy, S, 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

Arrow of time

• 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)
• Steven F. Savitt (Ed.) "Time's Arrows Today: Recent Physical and Philosophical Work on the Direction of Time", Cambridge University Press

See also:

• Entropy of a glass
• Shannon entropy
• Tsallis entropy
• H-theorem

Interesting reading

• E. T. Jaynes "Gibbs vs Boltzmann Entropies", American Journal of Physics 33 pp. 391-398 (1965)
• S. F. Gull "Some Misconceptions about Entropy" in Brian Buck and Vincent A. MacAulay (Eds.) "Maximum Entropy in Action", Oxford Science Publications (1991)
• Karl K. Darrow "The Concept of Entropy", American Journal of Physics 12 pp. 183-196 (1944)
• Daniel F. Styer "Insight into entropy", American Journal of Physics 86 pp. 1090-1096 (2000)

References

1. William G. Hoover "Entropy for Small Classical Crystals", Journal of Chemical Physics 49 pp. 1981-1982 (1968)