Effects of error on fluctuations under feedback control

TL;DR

This paper investigates how measurement errors affect the violation of the fluctuation-dissipation theorem in feedback-controlled Brownian motion, establishing bounds on cooling limits and effective temperature.

Contribution

It introduces models showing the impact of measurement errors on FDT violation and derives analytical bounds on cooling limits in feedback systems.

Findings

FDT violation is bounded by mutual information with measurement errors

Analytical results for cooling limits in feedback-controlled systems

Lower bounds on effective temperature resemble Carnot efficiency

Abstract

We consider a one-dimensional Brownian motion under nonequilibrium feedback control. Generally, the fluctuation-dissipation theorem (FDT) is violated in driven systems under nonequilibrium conditions. We find that the degree of the FDT violation is bounded by the mutual information obtained by the feedback system when the feedback protocol includes measurement errors. We introduce two simple models to illustrate cooling processes by feedback control and demonstrate analytical results for the cooling limit in those systems. Especially in a steady state, lower bounds to the effective temperature are given by an inequality similar to the Carnot efficiency.