Unified framework for the entropy production and the stochastic interaction based on information geometry
Sosuke Ito, Masafumi Oizumi, Shun-ichi Amari
Abstract
This paper investigates a new formula of the total entropy production as an information-geometric projection. This formula also leads the definition of the partial entropy production for the subsystem introduced in the context of Maxwell's demon. To compare the total entropy production with the partial entropy production from the viewpoint of information geometry, the authors find a connection between the entropy production and the stochastic interaction, which is a measure of information integration.
Topics & Concepts
Entropy productionMathematicsEntropy (arrow of time)Joint quantum entropyInformation diagramJoint entropyGeneralized relative entropyMaximum entropy probability distributionTransfer entropyEntropy rateQuantum relative entropyComplete informationMaximum entropy thermodynamicsInformation theoryProduction (economics)Principle of maximum entropyBinary entropy functionMaximum entropy spectral estimationKullback–Leibler divergenceStochastic processStatistical physicsMathematical optimizationApplied mathematicsComputer scienceInformation geometryBoltzmann's entropy formulaMeasure (data warehouse)Conditional entropyDifferential entropyRényi entropyH-theoremAdvanced Thermodynamics and Statistical MechanicsStatistical Mechanics and EntropyControl and Stability of Dynamical Systems