Thermodynamic aspects of information transfer in complex dynamical systems

From the Horowitz-Esposito stochastic thermodynamical description of information flows in dynamical systems [J. M. Horowitz and M. Esposito, Phys. Rev. X 4, 031015 (2014)], it is known that while the second law of thermodynamics is satisfied by a joint system, the entropic balance for the subsystems is adjusted by a term related to the mutual information exchange rate between the two subsystems. In this article, we present a quantitative discussion of the conceptual link between the Horowitz-Esposito analysis and the Liang-Kleeman work on information transfer between dynamical system components [X. S. Liang and R. Kleeman, Phys. Rev. Lett. 95, 244101 (2005)]. In particular, the entropic balance arguments employed in the two approaches are compared. Notwithstanding all differences between the two formalisms, our work strengthens the Liang-Kleeman heuristic balance reasoning by showing its formal analogy with the recent Horowitz-Esposito thermodynamic balance arguments.