Exact coarse-graining preserves entropy production out of equilibrium

The entropy production rate associated to broken time-reversal symmetry provides an essential characterization of nano-systems out of equilibrium, from driven colloidal particles to molecular motors. Limited access to the dynamical states is generally expected to hinder the correct estimation of this observable. Here we show how memoryless jump processes can be coarse-grained exactly preserving its average and fluctuations at stationarity. This supports univocal applicability of fluctuation theorems for entropy and allows inference of the genuine thermodynamics together with inaccessible process details.