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For Brownian motion of a single particle subject to a tilted periodicpotential on a ring, we propose a formula for experimentally determining thecumulant generating function of time-averaged current without measurements ofcurrent fluctuations. We first derive this formula phenomenologically on thebasis of two key relations: a fluctuation relation associated with Onsager'sprinciple of the least energy dissipation in a sufficiently local region and anadditivity relation by which spatially inhomogeneous fluctuations can beproperly considered. We then derive the formula without any phenomenologicalassumptions. We also demonstrate its practical advantage by numericalexperiments.

Variational formula for experimental determination of high-order correlations of current fluctuations in driven systems