  The minimum entropy production principle provides an approximative
variational characterization of close-to-equilibrium stationary states, both
for macroscopic systems and for stochastic models. Analyzing the fluctuations
of the empirical distribution of occupation times for a class of Markov
processes, we identify the entropy production as the large deviation rate
function, up to leading order when expanding around a detailed balance
dynamics. In that way, the minimum entropy production principle is recognized
as a consequence of the structure of dynamical fluctuations, and its
approximate character gets an explanation. We also discuss the subtlety
emerging when applying the principle to systems whose degrees of freedom change
sign under kinematical time-reversal.
