Convergence to equilibrium for many particle systems

TL;DR

This paper reviews recent results on the ergodic behavior of classical and quantum many-particle systems, proposing a new formulation of Boltzmann's ergodicity hypothesis based on minimal external contact.

Contribution

It introduces a novel perspective that minimal, memoryless external contact with one particle can ensure ergodicity in many-particle systems.

Findings

Almost all potentials lead to ergodicity with minimal external contact.

Memoryless contact is crucial for ergodicity.

New quantum results are also presented.

Abstract

The goal of this paper is to give a short review of recent results of the authors concerning classical Hamiltonian many particle systems. We hope that these results support the new possible formulation of Boltzmann's ergodicity hypothesis which sounds as follows. For almost all potentials, the minimal contact with external world, through only one particle of $N$, is sufficient for ergodicity. But only if this contact has no memory. Also new results for quantum case are presented.