Quantum mechanical evolution towards thermal equilibrium

TL;DR

This paper proves that quantum systems universally tend to equilibrium states when interacting with large environments, providing broad theoretical insights into quantum thermalization.

Contribution

It establishes general conditions under which quantum systems reach equilibrium, advancing understanding of quantum thermalization from fundamental principles.

Findings

Almost any subsystem reaches equilibrium with a large bath.

Equilibrium state is independent of the bath's micro-state.

Reaches equilibrium for nearly all times.

Abstract

The circumstances under which a system reaches thermal equilibrium, and how to derive this from basic dynamical laws, has been a major question from the very beginning of thermodynamics and statistical mechanics. Despite considerable progress, it remains an open problem. Motivated by this issue, we address the more general question of equilibration. We prove, with virtually full generality, that reaching equilibrium is a universal property of quantum systems: Almost any subsystem in interaction with a large enough bath will reach an equilibrium state and remain close to it for almost all times. We also prove several general results about other aspects of thermalisation besides equilibration, for example, that the equilibrium state does not depend on the detailed micro-state of the bath.