# Convergence to equilibrium due to collisions with external particles

## TL;DR

This paper demonstrates that in certain non-ergodic particle systems, ergodicity can be achieved when a single particle interacts randomly with external particles, highlighting a minimal external influence needed for equilibrium.

## Contribution

It introduces a novel analysis showing that ergodicity emerges in highly non-ergodic systems with just one particle having external contact, expanding understanding of system equilibration.

## Key findings

- Ergodicity appears in non-ergodic systems with external contact.
- A single particle's random collisions can induce system-wide equilibrium.
- The results apply to a class of 'most non ergodic' particle systems.

## Abstract

We consider a class of "most non ergodic" particle systems and prove that for most of them ergodicity appears if only one particle of N has contact with external world, that is this particle collides with external particles in random time moments.