A cycle decomposition and entropy production for circulant quantum Markov semigroups

TL;DR

This paper introduces a cycle decomposition framework for circulant quantum Markov semigroups, enabling explicit calculation of quantum entropy production rate and linking detailed balance to zero entropy production.

Contribution

It defines cycle representation and quantum entropy production rate for circulant quantum Markov semigroups, providing explicit formulas and conditions for quantum detailed balance.

Findings

Quantum detailed balance holds iff the quantum entropy production rate is zero.

Explicit computation of quantum entropy production rate for circulant qms.

Circulant qms can have non-equilibrium steady states with symmetries.

Abstract

We propose a definition of cycle representation for quantum Markov semigroups (qms) and quantum entropy production rate (qepr) in terms of the $\rho$-adjoint. We introduce the class of circulant qms, which admit non-equilibrium steady states but exhibit symmetries that allow us to compute explicitly the qepr, gain a deeper insight into the notion of cycle decomposition and prove that quantum detailed balance holds if and only if the qepr equals zero.