Entropy production and detailed balance for a class of quantum Markov semigroups

TL;DR

This paper derives an explicit entropy production formula for a class of quantum Markov semigroups related to weak system-reservoir coupling, linking detailed balance conditions to their constituent generators.

Contribution

It provides a novel explicit entropy production formula for quantum Markov semigroups and characterizes detailed balance in terms of their component generators.

Findings

Entropy production formula explicitly derived for the class of semigroups.

Quantum detailed balance condition characterized by component generators.

Semigroup detailed balance linked to invariance under component generators.

Abstract

We give an explicit entropy production formula for a class of quantum Markov semigroups, arising in the weak coupling limit of a system coupled with reservoirs, whose generators $\mathcal{L}$ are sums of other generators $\mathcal{L}_\omega$ associated with positive Bohr frequencies $\omega$ of the system. As a consequence, we show that any such semigroup satisfies the quantum detailed balance condition with respect to an invariant state if and only if all semigroups generated by each $\mathcal{L}_\omega$ so do with respect to the same invariant state.