Links between Dissipation and R\'{e}nyi Divergences in $\mathcal{PT}$-Symmetric Quantum Mechanics

TL;DR

This paper explores how the relationship between dissipated work and Rènyi divergences extends to PT-symmetric quantum mechanics, highlighting differences between unbroken and broken PT-symmetry regimes with experimental implications.

Contribution

It generalizes the connection between dissipated work and Rènyi divergences to PT-symmetric quantum systems with unbroken symmetry, and analyzes the breakdown of this relation in broken symmetry regimes.

Findings

Relation holds in unbroken PT-symmetry regime

Relation breaks down in broken PT-symmetry regime

Experimental system of two-coupled cavities illustrates the theory

Abstract

Thermodynamics and information theory have been intimately related since the times of Maxwell and Boltzmann. Recently it was shown that the dissipated work in an arbitrary non-equilibrium process is related to the R\'{e}nyi divergences between two states along the forward and reversed dynamics. Here we show that the relation between dissipated work and Renyi divergences generalizes to $\mathcal{PT}$-symmetric quantum mechanics with unbroken $\mathcal{PT}$ symmetry. In the regime of broken $\mathcal{PT}$ symmetry, the relation between dissipated work and Renyi divergences does not hold as the norm is not preserved during the dynamics. This finding is illustrated for an experimentally relevant system of two-coupled cavities.