Classical Geometric Fluctuation Relations

By defining an analogous stochastic quantity called Stochastic Fisher Information (SFI), we uncover two fluctuation relations with an inherent geometric nature, as the SFI acts as a single nonequilibrium trajectory metric. The geometric nature of these relations is expressed through a stochastic length derived from the system entropy associated with a nonequilibrium trajectory. We also explore the possibility of trajectory-dependent uncertainty relations linked to the time SFI. Finally, we test the newly discovered relations using two simple stochastic models.
Comment: Main text w/ 4.5 pages, Supplemental Material w/ 2 pages, 80 references/footnotes and No figures