  Systems out of equilibrium exhibit a net production of entropy. We study the
dynamics of a stochastic system represented by a Master Equation that can be
modeled by a Fokker-Planck equation in a coarse-grained, mesoscopic
description. We show that the corresponding coarse-grained entropy production
contains information on microscopic currents that are not captured by the
Fokker-Planck equation and thus cannot be deduced from it. We study a
discrete-state and a continuous-state system, deriving in both the cases an
analytical expression for the coarse-graining corrections to the entropy
production. This result elucidates the limits in which there is no loss of
information in passing from a Master Equation to a Fokker-Planck equation
describing the same system. Our results are amenable of experimental
verification, which could help to infer some information about the underlying
microscopic processes.
