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

TL;DR

This paper introduces a time-symmetric current in stochastic thermodynamics, demonstrating its fluctuation-response relation around nonequilibrium stalling states, providing a new experimental tool for measuring transition rates.

Contribution

It defines a novel time-symmetric current and proves its fluctuation-response relation holds beyond equilibrium, around nonequilibrium stationary states at stalling.

Findings

Fluctuation-response relation holds for the time-symmetric current.

Relation applies around nonequilibrium stalling stationary states.

Enables measurement of transition rates from empirical data.

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.