Time irreversibility from symplectic non-squeezing

TL;DR

This paper explores how the symplectic non-squeezing theorem provides a new perspective on the emergence of macroscopic irreversibility from microscopic reversible Hamiltonian dynamics, connecting classical physics concepts.

Contribution

It introduces a novel approach linking symplectic geometry to the problem of time irreversibility in Hamiltonian systems, extending Boltzmann's ideas with Gibbs's framework.

Findings

Symplectic non-squeezing constrains Hamiltonian evolution.

Macroscopic irreversibility can be derived from symplectic constraints.

The approach offers a geometric perspective on thermodynamic irreversibility.

Abstract

The issue of how time reversible microscopic dynamics gives rise to macroscopic irreversible processes has been a recurrent issue in Physics since the time of Boltzmann whose ideas shaped, and essentially resolved, such an apparent contradiction. Following Boltzmann's spirit and ideas, but employing Gibbs's approach, we advance the view that macroscopic irreversibility of Hamiltonian systems of many degrees of freedom can be also seen as a result of the symplectic non-squeezing theorem.