Unified framework for the entropy production and the stochastic interaction based on information geometry

TL;DR

This paper establishes a unified information geometric framework linking entropy production in stochastic thermodynamics with stochastic interaction, providing new insights into the thermodynamic foundation of integrated information theory.

Contribution

It introduces an information geometric interpretation of entropy production and relates the violation of additivity to stochastic interaction, advancing the theoretical understanding of thermodynamics and information integration.

Findings

New geometric interpretation of entropy production

Relation between entropy production additivity violation and stochastic interaction

Analytical illustration using the spin model

Abstract

We show a relationship between the entropy production in stochastic thermodynamics and the stochastic interaction in the information integrated theory. To clarify this relationship, we newly introduce an information geometric interpretation of the entropy production for a total system and the partial entropy productions for subsystems. We show that the violation of the additivity of the entropy productions is related to the stochastic interaction. This framework is a thermodynamic foundation of the integrated information theory. We also show that our information geometric formalism leads to a novel expression of the entropy production related to an optimization problem minimizing the Kullback-Leibler divergence. We analytically illustrate this interpretation by using the spin model.