Quantum mechanical evolution towards thermal equilibrium

Research output: Contribution to journalArticle (Academic Journal)peer-review

432 Citations (Scopus)


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 thermalization besides equilibration, for example, that the equilibrium state does not depend on the detailed microstate of the bath.

Original languageEnglish
Article number061103
Number of pages12
JournalPhysical Review E: Statistical, Nonlinear, and Soft Matter Physics
Issue number6
Publication statusPublished - Jun 2009

Bibliographical note

Publisher: APS


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