A general fluctuation-response relation for noise variations and its application to driven hydrodynamic experiments

TL;DR

This paper derives a fluctuation-response relation linking noise amplitude changes to unperturbed system behavior, demonstrated through hydrodynamic experiments with colloids, improving previous models by eliminating discretization dependence.

Contribution

It introduces a generalized fluctuation-response relation applicable to systems with additive noise, including those with nontrivial diffusivity matrices, and demonstrates its experimental and numerical utility.

Findings

Derived a fluctuation-response relation for noise variations in overdamped systems.

Validated the relation with hydrodynamic colloid experiments.

The scheme is numerically implementable and discretization-independent.

Abstract

The effect of a change of noise amplitudes in overdamped diffusive systems is linked to their unperturbed behavior by means of a nonequilibrium fluctuation-response relation. This formula holds also for systems with state-independent nontrivial diffusivity matrices, as we show with an application to an experiment of two trapped and hydrodynamically coupled colloids, one of which is subject to an external random forcing that mimics an effective temperature. The nonequilibrium susceptibility of the energy to a variation of this driving is an example of our formulation, which improves an earlier version, as it does not depend on the time-discretization of the stochastic dynamics. This scheme holds for generic systems with additive noise and can be easily implemented numerically, thanks to matrix operations.