Mixing and irreversibility in classical mechanics

TL;DR

This paper investigates the origins of irreversibility in classical mechanics with mixing, proposing a new approach that links entropy to inter-system forces and eliminates the need for phase space coarse-graining.

Contribution

It introduces a novel method for analyzing irreversible dynamics in mixing systems, establishing a direct connection between thermodynamics and classical mechanics.

Findings

Entropy expressed through forces between systems

Elimination of phase space coarse-graining

Link between thermodynamics and classical mechanics

Abstract

The mechanism of irreversible dynamics in the systems with mixing is analyzed. The procedure of splitting of system on equilibrium subsystems and studying of dynamics of one of them under condition of its interaction with other subsystems in the basis of the approach to the analysis of dynamics of nonequilibrium systems is used. The problem of "coarse-grain" of the phase space in this method is eliminated. The formula, which expresses the entropy through the work of forces between systems, is submitted. The essential link between thermodynamics and classical mechanics was found.