  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.
