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 general lower bound on the steady-state entropy production is obtained. Two particular ensembles of perturbation fields are then considered, respectively constant gradients and density displacements, and correspondingly two different averaging-based thermodynamic bounds are derived from the integral relation. These provide feasible methods to estimate the steady-state entropy production from relaxation experiments.