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H-Theorems from Autonomous Equations

W. De Roeck·C. Maes·K. Netocny
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Abstract

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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W. De Roeck, C. Maes, K. Netocny. 2006-01-04. H-Theorems from Autonomous Equations. https://doi.org/10.1007/s10955-006-9079-x

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