Information Flows in Continuous-Time Stochastic System as Dynamical Causal Effects

Methods for estimation of directional (causal) couplings in complex systems from time series constitute a wide field of research with applications in different disciplines including physics, climate science, neuroscience, etc. Among multiple quantisers of causality, "information flows" (IFs) are defined in diverse ways, transfer entropy (TE) and Liang – Kleeman information flow (LKIF) are the most popular IFs with many interesting applications. So, their numerical relationships are of importance, but still far from being fully understood. The recently proposed framework of dynamical causal effects provides a unifying formalism for causality quantifiers which is a convenient tool to study such relationships. Within that framework, the present work reveals numerical relationships between the TE and the LKIF in an exemplary stochastic system of coupled noise-driven overdamped oscillators. Those relationships appear to be quite diverse, depending essentially on parameters of the system. The obtained results allow a better justified interpretation of the numerical values of both IFs that should make their practical applications more fruitful.