Kiwata Hirohito
Division of Natural Science, Osaka Kyoiku University, Kashiwara, Osaka 582-8582, Japan.
Phys Rev E. 2022 Apr;105(4-1):044130. doi: 10.1103/PhysRevE.105.044130.
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.
施赖伯转移熵是研究随机变量之间因果关系的重要指标。梁 - 克莱曼信息流是另一种用于证明动力系统内因果关系的分析方法。霍洛维茨信息流是通过多组分随机热力学引入的。在本研究中，我通过霍洛维茨信息流阐明了施赖伯转移熵与梁 - 克莱曼信息流之间的关系。我考虑了系统根据随机微分方程变化的情况。我发现梁 - 克莱曼信息流和霍洛维茨信息流相差一个由随机涨落导出的项。我还表明施赖伯转移熵不小于霍洛维茨信息流。这项研究有助于统一各种确定变量间因果关系的指标。
