Information flow and entropy production on Bayesian networks

TL;DR

This paper reviews a theoretical framework combining thermodynamics and information theory using Bayesian networks, highlighting how transfer entropy bounds entropy production in complex nonequilibrium systems.

Contribution

It introduces a generalized second law of thermodynamics incorporating transfer entropy, providing insights into information-driven entropy bounds in stochastic systems.

Findings

Transfer entropy quantifies directional information transfer.

The generalized second law sets a lower bound on entropy production.

Framework applies to complex, interacting nonequilibrium systems.

Abstract

In this article, we review a general theoretical framework of thermodynamics of information on the basis of Bayesian networks. This framework can describe a broad class of nonequilibrium dynamics of multiple interacting systems with complex information exchanges. For such situations, we discuss a generalization of the second law of thermodynamics including information contents. The key concept here is an informational quantity called the transfer entropy, which describes the directional information transfer in stochastic dynamics. The generalized second law gives the fundamental lower bound of the entropy production in nonequilibrium dynamics, and sheds modern light on the paradox of "Maxwell's demon" that performs measurements and feedback control at the level of thermal fluctuations.