Recurrence Theorems: a unified account

TL;DR

This paper unifies classical and quantum recurrence theorems, extending them to linear and metric space dynamics, and discusses their implications in statistical mechanics foundations.

Contribution

It provides a unified framework for classical and quantum recurrence theorems and extends their applicability to broader mathematical settings.

Findings

Unified treatment of classical and quantum recurrence theorems

Proved recurrence theorems for linear and metric space dynamics

Discussed applications in statistical mechanics foundations

Abstract

I discuss classical and quantum recurrence theorems in a unified manner, treating both as generalisations of the fact that a system with a finite state space only has so many places to go. Along the way I prove versions of the recurrence theorem applicable to dynamics on linear and metric spaces, and make some comments about applications of the classical recurrence theorem in the foundations of statistical mechanics.