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

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