Backward transfer entropy: Informational measure for detecting hidden Markov models and its interpretations in thermodynamics, gambling and causality

Abstract

The transfer entropy is a well-established measure of information flow, which quantifies directed influence between two stochastic time series and has been shown to be useful in a variety fields of science. Here we introduce the transfer entropy of the backward time series called the backward transfer entropy, and show that the backward transfer entropy quantifies how far it is from dynamics to a hidden Markov model. Furthermore, we discuss physical interpretations of the backward transfer entropy in completely different settings of thermodynamics for information processing and the gambling with side information. In both settings of thermodynamics and the gambling, the backward transfer entropy characterizes a possible loss of some benefit, where the conventional transfer entropy characterizes a possible benefit. Our result implies the deep connection between thermodynamics and the gambling in the presence of information flow, and that the backward transfer entropy would be useful as a novel measure of information flow in nonequilibrium thermodynamics, biochemical sciences, economics and statistics.

16 pages, 2 figures

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Cited by in corpus (14)

• Stochastic thermodynamic interpretation of information geometry
• Geometrical aspects of entropy production in stochastic thermodynamics based on Wasserstein distance
• Thermodynamics of Gambling Demons
• Geometric thermodynamics for the Fokker-Planck equation: Stochastic thermodynamic links between information geometry and optimal transport
• Unified framework for the entropy production and the stochastic interaction based on information geometry
• Information thermodynamics for interacting stochastic systems without bipartite structure
• Quantum Fluctuation Theorem under Continuous Measurement and Feedback
• Role of sufficient statistics in stochastic thermodynamics and its implication to sensory adaptation
• Phase transitions in optimal strategies for betting
• Experimentally probing entropy reduction via iterative quantum information transfer
• Information thermodynamics of financial markets: the Glosten-Milgrom model
• Thermodynamic role of main reaction pathway and multi-body information flow in membrane transport
• Transfer Entropy and Flow of Information in Two-Skyrmion System
• Gibbs Distribution From Sequentially Predictive Form of the Second Law