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 L ω associated with positive Bohr frequencies ω of the system. As a consequence, weshow 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 L ω so do with respect to the same invariant state.