Entropy production and coarse graining in Markov processes

We study the large time fluctuations of entropy production in Markov processes. In particular, we consider the effect of a coarse-graining procedure which decimates fast states with respect to a given time threshold. Our results provide strong evidence that entropy production is not directly affected by this decimation, provided that it does not entirely remove loops carrying a net probability current. After the study of some examples of random walks on simple graphs, we apply our analysis to a network model for the kinesin cycle, which is an important biomolecular motor. A tentative general theory of these facts, based on Schnakenberg's network theory, is proposed