Statistical mechanical theory of an oscillating isolated system. The relaxation to equilibrium

TL;DR

This paper develops a statistical mechanical theory showing that a specially defined nonequilibrium entropy in an isolated system varies within bounds set by thermodynamic entropy and behaves like a free entropic oscillator, with relaxation described by Fokker-Planck equations.

Contribution

It introduces a new nonequilibrium entropy functional for N-body systems and reveals its oscillatory behavior and bounded variation, extending Gibbs entropy concepts.

Findings

Nonequilibrium entropy is not constant and is bounded by thermodynamic entropy.

The entropy behaves as a free entropic oscillator.

Relaxation to equilibrium is described by Fokker-Planck type equations.

Abstract

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=0,......., 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.