Entropy production of quantum Markov semigroup associated with open quantum walks on the periodic graphs

In this paper, we compute the entropy production of quantum Markov semigroup associated with open quantum walks. The entropy production, for the classical as well as quantum systems, measures the deviation from the symmetry between the forward and backward processes. The detailed balance condition with respect to an invariant state is the condition for the symmetry of the dynamics. Here we consider the quantum Markov semigroups associated with open quantum walks on the periodic graphs. On the one hand, the model serves as a good example to study the quantum detailed balance condition and the entropy production. On the other hand, from the viewpoint of the dynamics itself, the concept of entropy production helps for a better understanding of the dynamics.