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 ${\tau }_{\mathrm{B}}:=h/(k_{\mathrm{B}}T)$. Therefore what needs to be explained is, not that macroscopic systems approach equilibrium, but that they do so slowly.

5 pages

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