Thermalization from a general canonical principle

TL;DR

This paper explores how isolated quantum many-body systems thermalize, showing that subsystems resemble microcanonical or generalized Gibbs ensembles rather than canonical ones, especially considering finite-size effects and initial conditions.

Contribution

It provides a more rigorous foundation for the canonical principle by analyzing density matrices and clarifies the nature of subsystem states after thermalization in finite systems.

Findings

Subsystems resemble microcanonical or generalized Gibbs ensembles post-thermalization.

Finite-size effects prevent subsystems from being truly canonical or thermal.

Thermalization behavior extends to coupled systems with different initial temperatures.

Abstract

We investigate the time evolution of a generic and finite isolated quantum many-body system starting from a pure quantum state. We find the kinematical general canonical principle proposed by Popescu-Short-Winter for statistical mechanics can be built in a more solid ground by studying the thermalization, i.e. comparing the density matrices themselves rather than the measures of distances. In particular, this allows us to explicitly identify that, from any instantaneous pure state after thermalization, the state of subsystem is like from a microcanonical ensemble or a generalized Gibbs ensemble, but neither a canonical nor a thermal ones due to finite-size effect. Our results are expected to bring the task of characterizing the state after thermalization to completion. In addition, thermalization of coupled systems with different temperatures corresponding to mixed initial states is studied.