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Relationship between Schreiber's transfer entropy and Liang-Kleeman information flow from the perspective of
1Division of Natural Science, Osaka Kyoiku University, Kashiwara, Osaka 582-8582, Japan.
Abstract:
Schreiber's transfer entropy is an important index for investigating the causal relationship between random variables. The Liang-Kleeman information flow is another analysis to demonstrate the causality within dynamical systems. Horowitz's information flow is introduced through multicomponent stochastic thermodynamics. In this study, I elucidate the relationship between Schreiber's transfer entropy and the Liang-Kleeman information flow through Horowitz's information flow. I consider the case in which the system changes according to the stochastic differential equation. I find that the Liang-Kleeman and Horowitz information flows differ by a term derived from the stochastic fluctuation. I also show that Schreiber's transfer entropy is not less than Horowitz's information flow. This study helps unify various indexes that determine the causal relationship between variables.
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