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

We show a relation between the entropy production in stochastic thermodynamics and the stochastic interaction in the integrated information theory. To clarify this relation, we 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 an 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.