Time-symmetric current and its fluctuation response relation around nonequilibrium stalling stationary state

Abstract: We propose a time-symmetric counterpart of the current in stochastic thermodynamics named time-symmetric current. This quantity is defined with empirical measures and thus is symmetric under time reversal, while its ensemble average reproduces the amount of average current. We prove that this time-symmetric current satisfies the fluctuation-response relation in the conventional form with sign inversion. Remarkably, this fluctuation-response relation holds not only around equilibrium states but also around nonequilibrium stationary states if observed currents stall. The obtained relation also serves as an experimental tool for calculating the value of a bare transition rate by measuring only time-integrated empirical measures.