Information Flow as an Emergent Property of Divergence in Phase-Space

Abstract: Recent developments have created the ability to quantify information flow among components that interact in a dynamical system, and have led to significant advances in characterizing the dependence between the variables involved. In particular, they have been used to characterize causal dependency and feedback using observations across diverse fields such as environment, climate, finance, and human health. What causes information flow among coupled components of a dynamical system? This fundamental question has remained unanswered so far. Here it is established that the information flow is an emergent response resulting from the divergence of trajectories in phase-space of a dynamical system. This finding shows that the dynamics encapsulated in the traditional expression of Liouville equation, which neglects this divergence, merely propagates the dependence encoded in the initial conditions. However, when this is not the case, the informational dependence between the components change creating an information flow. This finding has significant implications in a variety of fields, both for the interpretation of observational data for causal inference in natural dynamics, and design of systems with targeted informational dependency.