Information-geometric structure for chemical thermodynamics: An explicit construction of dual affine coordinates

TL;DR

This paper develops an information-geometric framework for chemical thermodynamics, introducing dual affine coordinates, a metric, and divergence expressed via chemical potentials, extending known ideal solutions to non-ideal and open systems.

Contribution

It explicitly constructs dual affine coordinate systems and extends the geometric structure to non-ideal and open chemical systems, generalizing stochastic thermodynamics concepts.

Findings

Constructed dual affine coordinate systems using reaction extents and affinities.

Derived a metric and divergence expressed with chemical potentials.

Identified a thermodynamic analog of the Hatano-Sasa excess entropy production.

Abstract

We construct an information-geometric structure for chemical thermodynamics, applicable to a wide range of chemical reaction systems including non-ideal and open systems. For this purpose, we explicitly construct dual affine coordinate systems, which completely designate an information-geometric structure, using the extent of reactions and the affinities of reactions as coordinates on a linearly-constrained space of amounts of substances. The resulting structure induces a metric and a divergence (a function of two distributions of amounts), both expressed with chemical potentials. These quantities have been partially known for ideal-dilute solutions, but their extensions for non-ideal solutions and the complete underlying structure are novel. The constructed geometry is a generalization of dual affine coordinates for stochastic thermodynamics. For example, the metric and the divergence are generalizations of the Fisher information and the Kullback-Leibler divergence. As an application, we identify the chemical-thermodynamic analog of the Hatano-Sasa excess entropy production using our divergence.