Geometric decomposition of entropy production into excess, housekeeping and coupling parts

TL;DR

This paper unifies two existing entropy production decompositions in nonequilibrium Langevin dynamics, introduces a geometric interpretation, and extends the framework to include a coupling term, supported by thermodynamic uncertainty relations and an illustrative example.

Contribution

It establishes a geometric connection between two entropy decomposition methods and introduces a new three-part decomposition including a coupling term.

Findings

Decomposition into excess, housekeeping, and coupling entropy parts.

Derivation of thermodynamic uncertainty relations for these parts.

Validation through a solvable dragged particle example.

Abstract

For a generic overdamped Langevin dynamics driven out of equilibrium by both time-dependent and nonconservative forces, the entropy production rate can be decomposed into two positive terms, termed excess and housekeeping entropy. However, this decomposition is not unique: There are two distinct decompositions, one due to Hatano and Sasa, the other one due to Maes and Neto\v{c}ny. Here, we establish the connection between these two decompositions and provide a simple, geometric interpretation. We show that this leads to a decomposition of the entropy production rate into three positive terms, which we call excess, housekeeping and coupling part, respectively. The coupling part characterizes the interplay between the time-dependent and nonconservative forces. We also derive thermodynamic uncertainty relations for the excess and housekeeping entropy in both the Hatano-Sasa and Maes-Neto\v{c}ny-decomposition and show that all quantities obey integral fluctuation theorems. We illustrate the decomposition into three terms using a solvable example of a dragged particle in a nonconservative force field.