Entropy

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Entropy was first described by Rudolf Julius Emanuel Clausius in 1865 (Ref. 1). The statistical mechanical desciption is due to Ludwig Eduard Boltzmann (Ref. ?).

1 Classical thermodynamics
2 Statistical mechanics
3 Arrow of time
4 See also:
5 Interesting reading
6 References

[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 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 $Ω$ (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