Extremely quick thermalization in a macroscopic quantum system for a typical nonequilibrium subspace

Abstract

The fact that macroscopic systems approach thermal equilibrium may seem puzzling, for example, because it may seem to conflict with the time-reversibility of the microscopic dynamics. We here prove that in a macroscopic quantum system for a typical choice of ‘nonequilibrium subspace’, any initial state indeed thermalizes, and in fact does so very quickly, on the order of the Boltzmann time ${{\tau }_{{\rm B}}}:=h/({{k}_{{\rm B}}}T)$ . Therefore what needs to be explained is, not that macroscopic systems approach thermal equilibrium, but that they do so slowly.

Keywords

• quick thermalization
• typical nonequilibrium subspace
• Boltzmann time