Thermodynamic uncertainty relation for quantum entropy production

TL;DR

This paper establishes a thermodynamic uncertainty relation for quantum entropy production, linking it to quantum observables' mean and variance, and extends classical TURs to quantum regimes.

Contribution

It introduces a quantum TUR for entropy production based on a new lower bound for quantum divergence, bridging stochastic and quantum thermodynamics.

Findings

Reproduces classical TURs in the absence of coherence

Provides a quantum divergence lower bound relevant for thermodynamics

Connects to quantum Cramér-Rao inequality

Abstract

In quantum thermodynamics, entropy production is usually defined in terms of the quantum relative entropy between two states. We derive a lower bound for the quantum entropy production in terms of the mean and variance of quantum observables, which we will refer to as a thermodynamic uncertainty relation (TUR) for the entropy production. In the absence of coherence between the states, our result reproduces classic TURs in stochastic thermodynamics. For the derivation of the TUR, we introduce a lower bound for a quantum generalization of the $\chi^2$ divergence between two states and discuss its implications for stochastic and quantum thermodynamics, as well as the limiting case where it reproduces the quantum Cram\'er-Rao inequality.