Nonequilibrium relaxation inequality on short timescales

An integral relation is derived from the Fokker-Planck equation which connects the steady-state probability currents with the dynamics of relaxation on short timescales in the limit of small perturbation fields. As a consequence of this integral relation, a lower bound on the steady-state entropy production is obtained. For the particular case of an ensemble of random perturbation fields of weak spatial gradient, a simpler bound is derived from the integral relation which provides a feasible method to estimate entropy production from relaxation experiments.