Unified Jarzynski and Sagawa-Ueda relations for Maxwell's demon

TL;DR

This paper demonstrates that the Jarzynski and Sagawa-Ueda relations coexist uniquely in a Newtonian mechanics-based Maxwell's demon model, emphasizing mutual information's fundamental role in thermodynamics and information theory.

Contribution

It establishes the simultaneous validity and uniqueness of these relations within a unified model, highlighting mutual information as the core thermodynamic quantity.

Findings

Jarzynski and Sagawa-Ueda relations hold simultaneously in the model.

The relations are uniquely decomposable, supporting their fundamental connection.

Mutual information is confirmed as the key quantity in thermodynamic processes.

Abstract

By using Newtonian mechanics, we construct a general model of Maxwell's demon, a system in which the engine and the memory interact only through the exchange of information. We show that the Jarzynski relation and the two Sagawa-Ueda relations hold simultaneously, and argue that they are the unique triplet which has a natural decomposition property. The uniqueness provides a strong support to the assertion that the mutual information is the key quantity.