Scaling of Entropy Production under Coarse Graining

Entropy production plays a fundamental role in the study of non-equilibrium systems by offering a quantitative handle on the degree of time-reversal symmetry breaking. It depends crucially on the degree of freedom considered as well as on the scale of description. It was hitherto unknown how the entropy production at one resolution of the degrees of freedom is related to the entropy production at another resolution. This relationship is of particular relevance to coarse grained and continuum descriptions of a given phenomenon. In this work, we derive the scaling of the entropy production under iterative coarse graining on the basis of the correlations of the underlying microscopic transition rates. Our approach unveils a natural criterion to distinguish equilibrium-like and genuinely non-equilibrium macroscopic phenomena based on the sign of the scaling exponent of the entropy production per mesostate.