  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.
