Origin of the Canonical Ensemble: Thermalization with Decoherence

TL;DR

This paper demonstrates that the canonical ensemble naturally emerges from pure quantum dynamics through decoherence, without relying on time-averaging or weak coupling assumptions, thus linking quantum mechanics to statistical mechanics.

Contribution

It provides a direct quantum dynamical derivation of the canonical ensemble from a spin system interacting with a spin bath, without approximations.

Findings

Environment induces decoherence and thermalization of the spin system.

Canonical ensemble states can arise purely from quantum dynamics.

Exception occurs if the system cannot exchange energy with the bath.

Abstract

We solve the time-dependent Schrodinger equation for the combination of a spin system interacting with a spin bath environment. In particular, we focus on the time development of the reduced density matrix of the spin system. Under normal circumstances we show that the environment drives the reduced density matrix to a fully decoherent state, and furthermore the diagonal elements of the reduced density matrix approach those expected for the system in the canonical ensemble. We show one exception to the normal case is if the spin system cannot exchange energy with the spin bath. Our demonstration does not rely on time-averaging of observables nor does it assume that the coupling between system and bath is weak. Our findings show that the canonical ensemble is a state that may result from pure quantum dynamics, suggesting that quantum mechanics may be regarded as the foundation of quantum statistical mechanics.