Thermodynamics with Continuous Information Flow

Abstract

We provide a unified thermodynamic formalism describing information transfers in autonomous as well as nonautonomous systems described by stochastic thermodynamics. We demonstrate how information is continuously generated in an auxiliary system and then transferred to a relevant system that can utilize it to fuel otherwise impossible processes. Indeed, while the joint system satisfies the second law, the entropy balance for the relevant system is modified by an information term related to the mutual information rate between the two systems. We show that many important results previously derived for nonautonomous Maxwell demons can be recovered from our formalism and use a cycle decomposition to analyze the continuous information flow in autonomous systems operating at a steady state. A model system is used to illustrate our findings.

Thermodynamic aspects of information transfer in complex dynamical systems

“…Specifically, they have considered a bipartite system (xy-system) where Maxwell's demon is one of the subsystems (y-system) that affects the other subsystem (x-system) used to extract work from a heat bath. Here we focus on the stochastic thermodynamical formalism used in [2] by Horowitz and Esposito to characterize how information flow influences the thermodynamics of a system described by a probability distribution that evolves according to a Markovian master equation [32] (or, more specially, a Fokker-Planck equation [33]). …”

“…In what follows, we limit our discussion to bipartite thermodynamics and information flow [2]. For a very recent analysis extended to multipartite flow, we refer to [5].…”

“…A similar type of hybrid information-theoretic and statistical physics approach, including reasonings based upon the second law, to the study of information flow in interacting systems has been recently discussed by Hartich-Barato-Seifert and Horowitz-Esposito in Refs. [23] and [2], respectively. More specifically, in [22] entropic rate is defined as the time derivative of the time-delayed mutual information and is used to characterize the information flow between two Brownian particles coupled to different heat baths, as mentioned earlier.…”

“…In [23], entropic rate is defined as the entropy reduction rate of a subsystem due to its coupling to the other subsystem composing the bipartite system and is used to show that Maxwell's demon can be realized in terms of a bipartite Markov process. Finally, in [2] entropic rate is defined as the time derivative of the mutual information and is used to investigate the thermodynamics of information flow between two interacting subsystems of a Markovian bipartite system.…”

“…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.…”