On the Second Law of thermodynamics and the piston problem

The piston problem is investigated in the case where the length of the cylinder is infinite (on both sides) and the ratio $m/M$ is a very small parameter, where $m$ is the mass of one particle of the gaz and $M$ is the mass of the piston. Introducing initial conditions such that the stochastic motio...

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Bibliographic Details
Published in:Journal of statistical physics 2004-11, Vol.117 (3-4), p.739-772
Main Authors: GRUBER, Christian, PACHE, Séverine, LESNE, Annick
Format: Article
Language:English
Subjects:
Condensed Matter
Exact sciences and technology
Physics
Statistical Mechanics
Statistical physics, thermodynamics, and nonlinear dynamical systems
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Summary:The piston problem is investigated in the case where the length of the cylinder is infinite (on both sides) and the ratio $m/M$ is a very small parameter, where $m$ is the mass of one particle of the gaz and $M$ is the mass of the piston. Introducing initial conditions such that the stochastic motion of the piston remains in the average at the origin (no drift), it is shown that the time evolution of the fluids, analytically derived from Liouville equation in a previous work, agrees with the Second Law of thermodynamics. We thus have a non equilibrium microscopical model whose evolution can be explicitly shown to obey the two laws of thermodynamics.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-004-2271-y