Nonequilibrium Thermodynamics of Feedback Control

TL;DR

This paper develops a comprehensive theoretical framework for feedback control in classical stochastic thermodynamics, extending nonequilibrium equalities to include multiple measurements and multiple heat baths, with implications for information thermodynamics.

Contribution

It generalizes nonequilibrium equalities like the fluctuation theorem and Jarzynski equality to systems with complex feedback and measurement scenarios.

Findings

Derived generalized fluctuation theorems with measurement and feedback terms

Validated equalities using models like Szilard engine and feedback ratchet

Extended thermodynamic relations to multi-heat bath systems

Abstract

We establish a general theory of feedback control on classical stochastic thermodynamic systems, and generalize nonequilibrium equalities such as the fluctuation theorem and the Jarzynski equality in the presence of feedback control with multiple measurements. Our results are generalizations of the previous relevant works to the situations with general measurements and multi-heat baths. The obtained equalities involve additional terms that characterize the information obtained by measurements or the efficacy of feedback control. A generalized Szilard engine and a feedback-controlled ratchet are shown to satisfy the derived equalities.