Finite sampling effects on generalized fluctuation-dissipation relations for steady states

TL;DR

This paper investigates how finite data samples affect the accuracy of generalized fluctuation-dissipation relations in nonequilibrium steady states, proposing correction methods to improve experimental estimates.

Contribution

It identifies two key effects of finite sampling on fluctuation-dissipation measurements and introduces an estimator to correct initial sampling errors, validating the approach experimentally.

Findings

Finite sampling can impair the estimation of response functions.

Introducing an estimator corrects initial sampling errors.

The corrected method verifies the fluctuation-dissipation relation experimentally.

Abstract

We study the effects of the finite number of experimental data on the computation of a generalized fluctuation-dissipation relation around a nonequilibrium steady state of a Brownian particle in a toroidal optical trap. We show that the finite sampling has two different effects, which can give rise to a poor estimate of the linear response function. The first concerns the accessibility of the generalized fluctuation-dissipation relation due to the finite number of actual perturbations imposed to the control parameter. The second concerns the propagation of the error made at the initial sampling of the external perturbation of the system. This can be highly enhanced by introducing an estimator which corrects the error of the initial sampled condition. When these two effects are taken into account in the data analysis, the generalized fluctuation-dissipation relation is verified experimentally.