Thermodynamic constraints on kinetic perturbations of homogeneous driven diffusions

We analyze the static response to kinetic perturbations of nonequilibrium steady states that can be modeled as diffusions. We demonstrate that kinetic response is purely a nonequilibirum effect, measuring the degree to which the Fluctuation-Dissipation Theorem is violated out of equilibrium. For driven diffusions in a flat landscape, we further demonstrate that such response is constrained by the strength of the nonequilibrium driving via quantitative inequalities.