Equilibrium trajectories quantify second order violation of fluctuation dissipation theorem without need of a model

TL;DR

This paper introduces a series expansion that quantifies second-order violations of the fluctuation dissipation theorem in driven classical systems, validated through experiments with a Brownian particle in complex fluids.

Contribution

It presents a novel series expansion relating non-equilibrium cumulants, valid across scales, and confirms its experimental applicability without requiring a specific model.

Findings

Series expansion matches experimental data for a driven Brownian particle.

The form of the fluctuation dissipation theorem remains valid for Gaussian observables away from equilibrium.

Expansion aligns with known fluctuation theorem up to moments versus cumulants differences.

Abstract

Quantifying and characterizing fluctuations far away from equilibrium is a challenging task. We discuss and experimentally confirm a series expansion for a driven classical system, relating the different non-equilibrium cumulants of the observable conjugate to the driving protocol. This series is valid from micro- to macroscopic length scales, and it encompasses the fluctuation dissipation theorem. We apply it in experiments of a Brownian probe particle confined and driven by an optical potential and suspended in a nonlinear and non-Markovian fluid. The expansion states that the form of FDT remains valid away from equilibrium for Gaussian observables, up to the order presented. We show that this expansion agrees with the expansion of a known fluctuation theorem up to an unresolved difference regarding moments versus cumulants.