H-Theorems from Macroscopic Autonomous Equations |
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Authors: | Wojciech De Roeck Christian Maes Karel Netočný |
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Institution: | (1) Instituut voor Theoretische fysica, K.U. Leuven, Leuven, Belgium;(2) Institute of Physics As CR, Prague, Czech |
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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 rigourously establish the connection with macroscopic autonomy.If for a Hamiltonian dynamics for many particles, the macrostate evolves autonomously, 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 semigroup property for the macroscopic evolution. |
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Keywords: | H-theorem entropy irreversible equations |
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