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

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.Comment: 13pages, 4 figure

A unified framework for information integration based on information geometry

We propose a unified theoretical framework for quantifying spatio-temporal interactions in a stochastic dynamical system based on information geometry. In the proposed framework, the degree of interactions is quantified by the divergence between the actual probability distribution of the system and a constrained probability distribution where the interactions of interest are disconnected. This framework provides novel geometric interpretations of various information theoretic measures of interactions, such as mutual information, transfer entropy, and stochastic interaction in terms of how interactions are disconnected. The framework therefore provides an intuitive understanding of the relationships between the various quantities. By extending the concept of transfer entropy, we propose a novel measure of integrated information which measures causal interactions between parts of a system. Integrated information quantifies the extent to which the whole is more than the sum of the parts and can be potentially used as a biological measure of the levels of consciousness