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Statistical mechanical theory of an oscillating isolated system: The relaxation to equilibrium
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In this Contribution we show that a suitably defined nonequilibrium entropy of an N-body isolated system is not a constant of the motion, in general, and its variation is bounded, the bounds determined by the thermodynamic entropy, i.e., the equilibrium entropy. We define the nonequilibrium entropy as a convex functional of the set of n-particle reduced distribution functions (n ? N) generalizing the Gibbs fine-grained entropy formula. Additionally, as a consequence of our microscopic analysis we find that this nonequilibrium entropy behaves as a free entropic oscillator. In the approach to the equilibrium regime, we find relaxation equations of the Fokker-Planck type, particularly for the one-particle distribution function.
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PÉREZ MADRID, Agustín. Statistical mechanical theory of an oscillating isolated system: The relaxation to equilibrium. _Journal of Mathematical Physics_. 2007. Vol. 48, núm. 103302. [consulta: 20 de gener de 2026]. ISSN: 0022-2488. [Disponible a: https://hdl.handle.net/2445/24584]