Recurrence Theorems: a unified account
David Wallace

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.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Quantum Mechanics and Applications · Computability, Logic, AI Algorithms
