Information Transfer between Dynamical System Components

Abstract

We present a rigorous formalism of information transfer for systems with dynamics fully known. This follows from an accurate classification of the mechanisms for the entropy change of one component into a self-evolution plus a transfer from the other component. The formalism applies to both continuous flows and discrete maps. The resulting transfer measure possesses a property of asymmetry and is qualitatively consistent with the classical measures. It is further validated with the baker transformation and the Hénon map.

Thermodynamic aspects of information transfer in complex dynamical systems

“…(13), (21), and (19) within the HorowitzEsposito approach, respectively. Due to these conceptual and mathematical analogies, the heuristic entropic balance arguments in [6] are automatically supported by the thermodynamically grounded entropic balance arguments as presented in [2]. One of our main contributions in this article is pointing out these hidden connections after a critical reconsideration of both approaches.…”

“…(1), (3), and (13)), we presented a quantitative discussion on the physical link between the Horowitz-Esposito analysis [2] and the Liang-Kleeman work on information transfer between dynamical system components [6]. In particular, the entropic balance arguments employed in the two approaches were compared.…”

“…For the latest developments on this approach, we refer instead to [29]. In this article, our discussion is based upon the working hypotheses of the original work presented in [6] which contains the essence of the philosophy of the Liang-Kleeman approach. Specifically, we shall be considering a two-dimensional continuous and deterministic autonomous system with a priori knowledge of the dynamics,…”

“…systems is justified by the important role that information transfer analysis has in detecting asymmetry in the interaction of subsystems [1], in predicting the weather [6], in controlling a system [7,8], in inferring causal structures [9,10], and, from a more conceptual standpoint, in investigating the thermodynamics of Maxwell's demon [11][12][13].…”

“…Instead, inspired by the works in [2,22,23], we focus on two main points in this article. First, we point out the conceptual link between the Liang-Kleeman notion of information transfer [6] and the Horowitz-Esposito notion of information flow [2]. This allows us to avoid some heuristic arguments in the Liang-Kleeman approach and replace them with thermodynamic reasoning.…”