Exact Identity Linking Entropy Production and Mutual Information

Abstract

We establish an exact identity for overdamped Langevin dynamics: the total entropy production rate equals four times the mutual information rate between an infinitesimal displacement and its time midpoint, plus a mean flow term. This yields a forward-only characterization of irreversibility. As a corollary, for additive bipartite systems, the chain rule directly yields a canonical nonnegative decomposition of subsystem entropy production into self and interaction components. The self term coincides with apparent entropy production, while the interaction term captures the dissipative cost of dependence and sharpens the learning rate bound. In a proof-of-concept application to red blood cell flickering, the decomposition reveals the thermodynamic structure of mechanical irreversibility. Overall, our results recast entropy production as a decomposable information-theoretic structure.