Temporal Behavior of the Conditional and Gibbs' Entropies

Details Temporal Behavior of the Conditional and Gibbs' Entropies Temporal Behavior of the Conditional and Gibbs' Entropies

2005-09-26

arxiv.org/abs/cond-mat/0509649v1

Journal of Statistical Physics 124 (2006) 1443-1470.

Physics

Condensed Matter

Statistical Mechanics

15 pages, 5 figures

Scientific paper

10.1007/s10955-006-9181-0

We study the temporal approach to equilibrium of the Gibbs' and conditional entropies for both invertible deterministic dynamics as well as non-invertible stochastic systems in the presence of white noise. The conditional entropy will either remain constant or monotonically increase to its maximum of zero. However, the Gibbs' entropy may have a variety of patterns of approach to its final value ranging from a monotone increase or decrease to an oscillatory approach. We have illustrated all of these behaviors using examples in which both entropy dynamics can be determined analytically.

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