Fluctuation Relations for Heat Exchange in the Generalized Gibbs Ensemble

TL;DR

This paper extends fluctuation relations for heat exchange to quantum systems in the generalized Gibbs ensemble, linking heat exchange to Rénnyi divergences and applicable across integrable and chaotic regimes.

Contribution

It generalizes fluctuation relations for heat exchange to systems described by the generalized Gibbs ensemble and connects these to Rénnyi divergences for broad initial conditions.

Findings

Fluctuation relations are valid for quantum systems with conserved quantities.

Relations apply universally to integrable and chaotic quantum regimes.

Connects heat exchange to Rénnyi divergences in generalized Gibbs states.

Abstract

In this work, we investigate the heat exchange between two quantum systems whose initial equilibrium states are described by the generalized Gibbs ensemble. First, we generalize the fluctuation relations for heat exchange discovered by Jarzynski and W\'ojcik to quantum systems prepared in the equilibrium states described by the generalized Gibbs ensemble at different generalized temperatures. Second, we extend the connections between heat exchange and R\'enyi divergences to quantum systems with very general initial conditions.These relations are applicable for quantum systems with conserved quantities and are universally valid for quantum systems in the integrable and chaotic regimes.