Inflow rate, a time-symmetric observable obeying fluctuation relations

TL;DR

This paper introduces fluctuation relations for time-symmetric observables like inflow rate in mesoscopic systems, linking deterministic and stochastic dynamics and expanding the scope of fluctuation theorems beyond entropy-related quantities.

Contribution

It derives detailed and integral fluctuation relations for inflow rate, a time-symmetric quantity, establishing a formal connection between reversible and irreversible systems.

Findings

Fluctuation relations hold for inflow rate in mesoscopic jump systems.

Inflow rate relates to phase space contraction and divergence of forces.

Results unify deterministic and stochastic descriptions under fluctuation theorems.

Abstract

While entropy changes are the usual subject of fluctuation theorems, we seek fluctuation relations involving time-symmetric quantities, namely observables that do not change sign if the trajectories are observed backward in time. We find detailed and integral fluctuation relations for the (time integrated) difference between "entrance rate" and escape rate in mesoscopic jump systems. Such "inflow rate", which is even under time reversal, represents the discrete-state equivalent of the phase space contraction rate. Indeed, it becomes minus the divergence of forces in the continuum limit to overdamped diffusion. This establishes a formal connection between reversible deterministic systems and irreversible stochastic ones, confirming that fluctuation theorems are largely independent of the details of the underling dynamics.