Geometry of Nonequilibrium Chemical Reaction Networks and Generalized Entropy Production Decompositions

TL;DR

This paper develops a Hessian geometric framework for nonequilibrium chemical reaction networks, enabling generalized entropy production decompositions that extend classical theories to more complex, nonquadratic dissipation functions.

Contribution

It introduces a Hessian geometric structure for CRNs and derives new entropy production decompositions applicable to nonquadratic dissipation functions.

Findings

Hessian geometry characterizes CRN dynamics as generalized flows.

Two new entropy production decompositions are proposed.

Framework extends classical theories to broader dissipation functions.

Abstract

We derive the Hessian geometric structure of nonequilibrium chemical reaction networks (CRN) on the flux and force spaces induced by the Legendre duality of convex dissipation functions and characterize their dynamics as a generalized flow. With this structure, we can extend theories of nonequilibrium systems with quadratic dissipation functions to more general ones with nonquadratic ones, which are pivotal for studying chemical reaction networks. By applying generalized notions of orthogonality in Hessian geometry to chemical reaction networks, we obtain two generalized decompositions of the entropy production rate, each of which captures gradient-flow and minimum-dissipation aspects in nonequilibrium dynamics.