H-Theorems from Autonomous Equations

Details H-Theorems from Autonomous Equations H-Theorems from Autonomous Equations

2005-08-03

arxiv.org/abs/cond-mat/0508089v2

J. Stat. Phys. 123:571-584 (2006)

Physics

Condensed Matter

Statistical Mechanics

13 pages; v1 -> v2: Sec. 1-2 considerably rewritten, minor corrections in Sec. 3-4

Scientific paper

The H-theorem is an extension of the Second Law to a time-sequence of states that need not be equilibrium ones. In this paper we review and we rigorously establish the connection with macroscopic autonomy. If for a Hamiltonian dynamics for many particles, at all times the present macrostate determines the future macrostate, then its entropy is non-decreasing as a consequence of Liouville's theorem. That observation, made since long, is here rigorously analyzed with special care to reconcile the application of Liouville's theorem (for a finite number of particles) with the condition of autonomous macroscopic evolution (sharp only in the limit of infinite scale separation); and to evaluate the presumed necessity of a Markov property for the macroscopic evolution.

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