Kinetic equality for susceptibility and dynamical activity

Response to an external perturbation characterizes the fundamental nature of equilibrium and nonequilibrium systems. The response properties have been expressed by the susceptibility and the precision given by the signal to noise ratio. In this Letter, we first derive a general response equality for precision that connects susceptibilities out of equilibrium for general observables to the Fisher information measuring a sensitivity to the perturbation. In particular, this fundamental result provides kinetic equality for susceptibility (KSE), a model-independent general equality among experimentally accessible quantities such as the time derivative of observables, the dynamical activity, and fluctuation for generic nonequilibrium systems. As special limiting cases, KSE reproduces the kinetic uncertainty relation and its extensions to multiple variables. We also show an equality between the susceptibility and the observable-action covariance. Hence, KSE provides a master relation of these nonequilibrium relations.