Symmetry for the duration of entropy-consuming intervals

Abstract

We introduce the violation fraction υ as the cumulative fraction of time that a mesoscopic system spendsconsuming entropy at a single trajectory in phase space.We showthat the fluctuations of this quantity are describedin terms of a symmetry relation reminiscent of fluctuation theorems, which involve a function , which can beinterpreted as an entropy associated with the fluctuations of the violation fraction. The function, when evaluatedfor arbitrary stochastic realizations of the violation fraction, is odd upon the symmetry transformations that arerelevant for the associated stochastic entropy production. This fact leads to a detailed fluctuation theorem for theprobability density function of . We study the steady-state limit of this symmetry in the paradigmatic case of acolloidal particle dragged by optical tweezers through an aqueous solution. Finally, we briefly discuss possibleapplications of our results for the estimation of free-energy differences from single-molecule experiments.