Relationship between Schreiber's transfer entropy and Liang-Kleeman information flow from the perspective of stochastic thermodynamics

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.

Automated summary

This study clarifies the relationship between Schreiber's transfer entropy and Liang-Kleeman information flow through Horowitz's information flow, demonstrating their differences and showing that Schreiber's transfer entropy is not less than Horowitz's information flow.