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.
Highlights
Information geometry [1,2] is a differential geometric theory for elucidating various results in information theory and probability theory
We show a relation between the entropy production in stochastic thermodynamics and the stochastic interaction in the integrated information theory
By applying the information-geometric framework, we showed the relation between the entropy production and the stochastic interaction
Summary
Information geometry [1,2] is a differential geometric theory for elucidating various results in information theory and probability theory. We introduce a measure of information thermodynamics, namely, the partial entropy production for the subsystem. If two interacting dynamics are well separated, the sum of the partial entropy productions for each subsystem is equivalent to the total entropy production. This fact is known as the additivity of the entropy productions. We introduce several submanifolds related to backward dynamics, and the total entropy production and the partial entropy production can be considered to be given by the projections of the entire system onto these submanifolds. From the inclusion property of these submanifolds, we obtain a geometric interpretation of the additivity of the entropy productions This interpretation clarifies a relation between the violation of the additivity and the stochastic interaction. We analytically illustrate our results by using the spin models
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