Entropy Production and Detailed Balance for a Class of Quantum Markov Semigroups

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 L are sums of other generators Lw; associated with positive Bohr frequencies w; 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 Lw; do so with respect to the same invariant state.