Exact Identity Linking Entropy Production and Mutual Information

TL;DR

The paper derives an exact identity linking entropy production rate to mutual information rate in overdamped Langevin systems, providing a new information-theoretic perspective on irreversibility and subsystem dissipation.

Contribution

It introduces a novel exact identity connecting entropy production and mutual information, enabling a decomposable thermodynamic analysis of irreversibility.

Findings

Entropy production equals four times the mutual information rate plus a flow term.

Subsystem entropy production can be decomposed into self and interaction components.

Application to red blood cell flickering reveals thermodynamic irreversibility structure.

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.