Role of correlations in the thermalization of quantum systems

TL;DR

This paper studies how quantum systems reach thermal equilibrium, highlighting that minimal correlations and environmental changes promote thermalization, with a new map quantifying initial condition effects.

Contribution

Introduces a completely positive map to quantify the influence of initial conditions on quantum system thermalization, emphasizing the role of correlations and environmental stability.

Findings

Small system-environment correlations favor thermalization.

Minimal changes in the environment support equilibration.

The introduced map quantifies initial condition dependence.

Abstract

We investigate the equilibration and thermalization properties of quantum systems interacting with a finite dimensional environment. By exploiting the concept of time averaged states, we introduce a completely positive map which allows to describe in a quantitative way the dependence of the equilibrium state on the initial condition. Our results show that the thermalization of quantum systems is favored if the dynamics induces small system-environment correlations, as well as small changes in the environment, as measured by the trace distance.