Housekeeping and excess entropy production for general nonlinear dynamics

TL;DR

This paper introduces a new decomposition of entropy production for nonlinear discrete systems that separates contributions from external driving and conservative forces, applicable even in complex dynamical regimes.

Contribution

It presents a geometric, steady-state-independent decomposition of entropy production applicable to multistable, cyclic, and chaotic systems, extending thermodynamic uncertainty relations and speed limits.

Findings

Refines thermodynamic uncertainty relations.

Improves optimal-transport-based speed limits.

Extends transport theory to nonlinear, nonconservative systems.

Abstract

We propose a housekeeping/excess decomposition of entropy production for general nonlinear dynamics in a discrete space, including chemical reaction networks and discrete stochastic systems. We exploit the geometric structure of thermodynamic forces to define the decomposition; this does not rely on the notion of a steady state, and even applies to systems that exhibit multistability, limit cycles, and chaos. In the decomposition, distinct aspects of the dynamics contribute separately to entropy production: the housekeeping part stems from a cyclic mode that arises from external driving, generalizing Schnakenberg's cyclic decomposition to non-steady states, while the excess part stems from an instantaneous relaxation mode that arises from conservative forces. Our decomposition refines previously known thermodynamic uncertainty relations and speed limits. In particular, it not only improves an optimal-transport-theoretic speed limit, but also extends the optimal transport theory of discrete systems to nonlinear and nonconservative settings.