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

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.

arXiv comment13pages, 4 figures

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• Information Geometric Inequalities of Chemical Thermodynamics
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• Nonequilibrium diffusion processes via non-Hermitian electromagnetic quantum mechanics with application to the statistics of entropy production in the Brownian gyrator
• Nonequilibrium thermodynamics of the asymmetric Sherrington-Kirkpatrick model
• Complexity and efficiency of minimum entropy production probability paths from quantum dynamical evolutions
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• Speed-accuracy relations for diffusion models: Wisdom from nonequilibrium thermodynamics and optimal transport
• Inferring entropy production in many-body systems using nonequilibrium maximum entropy
• Entropy Production in the Inflationary Epoch Using the Gouy-Stodola Theorem
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• State-space kinetic Ising model reveals task-dependent entropy flow in sparsely active nonequilibrium neuronal dynamics
• Generalized free energy and excess/housekeeping decomposition in nonequilibrium systems: from large deviations to thermodynamic speed limits
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