Jarzynski Equality with Maxwell's Demon

TL;DR

This paper introduces a new thermodynamic equality and inequalities linking work and information in isothermal processes involving Maxwell's demon, using Jarzynski's formulation and quantum information theory.

Contribution

It presents a novel thermodynamic equality and inequalities that relate work, information gain, and measurement accuracy in Maxwell's demon scenarios.

Findings

Derived a lower bound on work based on information gain and measurement accuracy.

Results are valid regardless of the demon's thermodynamic state.

Established a framework connecting Jarzynski equality with Maxwell's demon.

Abstract

We propose a new thermodynamic equality and several inequalities concerning the relationship between work and information for an isothermal process with Maxwell's demon. Our approach is based on the formulation a la Jarzynski of the thermodynamic engine and on the quantum information-theoretic characterization of the demon. The lower bound of each inequality, which is expressed in terms of the information gain by the demon and the accuracy of the demon's measurement, gives the minimum work that can be performed on a single heat bath in an isothermal process. These results are independent of the state of the demon, be it in thermodynamic equilibrium or not.