Equilibrium trajectories quantify second-order violations of the fluctuation–dissipation theorem without the need for a model

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 nonequilibrium 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 (FDT). 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 the FDT remains valid away from equilibrium for Gaussian observables, up to the order presented. We show that this expansion agrees with that of a known fluctuation theorem up to an unresolved difference regarding moments versus cumulants.