Operator equality on entropy production in quantum Markovian master equations

TL;DR

This paper derives an operator equality for entropy production in quantum Markovian systems, revealing its connection to time-reversal asymmetry without relying on stochastic trajectories or prior definitions.

Contribution

It introduces a novel operator equality for quantum entropy production that does not depend on stochastic trajectories or prior quantum entropy definitions.

Findings

Operator equality relates to time-reversal asymmetry in quantum systems

First order expansion differs from classical mean entropy production

Highlights noncommutativity effects in quantum entropy dynamics

Abstract

An operator equality on the entropy production for general quantum Markovian master equations is derived without resorting quantum stochastic trajectory and priori quantum definition of entropy production. We find that, the equality can be still interpreted as a consequence of time-reversal asymmetry of the nonequilibrium processes of the systems. In contrast with the classical case, however, the first order expansion of the equality does not directly related to the mean entropy production, which arises from noncommute property of operators in quantum physics.