Equilibration of quantum systems and subsystems

TL;DR

This paper unifies recent results on quantum equilibration, demonstrating that both expectation values and small subsystems tend to equilibrium states under broad conditions, with implications for understanding quantum thermalization.

Contribution

It generalizes a proof of observable equilibration and re-derives a result on subsystem equilibration, unifying these findings in quantum theory.

Findings

Expectation values of realistic observables equilibrate broadly.

Small subsystems typically evolve to static equilibrium states.

Certain subspaces lead all initial states to the same equilibrium.

Abstract

We unify two recent results concerning equilibration in quantum theory. We first generalise a proof of Reimann [PRL 101,190403 (2008)], that the expectation value of 'realistic' quantum observables will equilibrate under very general conditions, and discuss its implications for the equilibration of quantum systems. We then use this to re-derive an independent result of Linden et. al. [PRE 79, 061103 (2009)], showing that small subsystems generically evolve to an approximately static equilibrium state. Finally, we consider subspaces in which all initial states effectively equilibrate to the same state.