Universal interpretation of efficacy parameter in perturbed nonequilibrium systems

TL;DR

This paper explores how feedback-modified fluctuation theorems can be universally interpreted through an efficacy parameter, providing consistent lower bounds on work in nonequilibrium systems regardless of feedback protocol design.

Contribution

It introduces a universal interpretation of the efficacy parameter in extended fluctuation theorems, ensuring consistent bounds on work in feedback-controlled nonequilibrium systems.

Findings

The efficacy parameter provides a consistent lower bound on work.

Different feedback protocols lead to varied correction terms in fluctuation theorems.

The proposed interpretation remains valid across multiple feedback schemes.

Abstract

The fluctuation theorems have remained one of the cornerstones in the study of systems that are driven far out of equilibrium, and they provide strong constraints on the fraction of trajectories that behave atypically in light of the second law. They have mainly been derived for a predetermined external drive applied to the system. However, to improve the efficiency of a process, one needs to incorporate protocols that are modified by receiving feedbacks about the recent state of the system, during its evolution. In such a case, the forms of the conventional fluctuation theorems get modified, the correction term involving terms that depend on the way the reverse/conjugate process is defined, namely, the rules of using feedback in order to generate the exact time-reversed/conjugate protocols. We show in this paper that this can be done in a large number of ways, and in each case we would get a different expression for the correction terms. This would in turn lead to several lower bounds on the mean work that must be performed on the system, or on the entropy changes. Here we analyze a form of the extended fluctuation theorems that involves the efficacy parameter, and find that this form gives rise to a lower bound for the mean work that retains a consistent physical meaning regardless of the design of feedback along the conjugate process, as opposed to the case of the previously mentioned form of the modified fluctuation theorems.