Role of Mutual Information in Entropy Production under Information Exchanges

TL;DR

This paper explores how information exchange influences entropy production in stochastic systems, deriving formulas that connect thermodynamics and information theory, applicable to various information processing scenarios.

Contribution

It introduces a general formula decomposing entropy production into thermodynamic and informational parts, extending fluctuation theorems to systems with multiple information exchanges.

Findings

Derivation of a unified entropy production formula including informational contributions

Extension of fluctuation theorems to systems with multiple information exchanges

Clarification of the dual relationship between measurement and feedback

Abstract

We relate the information exchange between two stochastic systems to the nonequilibrium entropy production in the whole system. By deriving a general formula that decomposes the total entropy production into the thermodynamic and informational parts, we obtain nonequilibrium equalities such as the fluctuation theorem in the presence of information processing. Our results apply not only to situations under measurement and feedback control, but also to those under multiple information exchanges between two systems, giving the fundamental energy cost for information processing and elucidating the thermodynamic and informational roles of a memory in information processing. We clarify a dual relationship between measurement and feedback.