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 spends<br />consuming entropy at a single trajectory in phase space.We showthat the fluctuations of this quantity are described<br />in terms of a symmetry relation reminiscent of fluctuation theorems, which involve a function , which can be<br />interpreted as an entropy associated with the fluctuations of the violation fraction. The function, when evaluated<br />for arbitrary stochastic realizations of the violation fraction, is odd upon the symmetry transformations that are<br />relevant for the associated stochastic entropy production. This fact leads to a detailed fluctuation theorem for the<br />probability density function of . We study the steady-state limit of this symmetry in the paradigmatic case of a<br />colloidal particle dragged by optical tweezers through an aqueous solution. Finally, we briefly discuss possible<br />applications of our results for the estimation of free-energy differences from single-molecule experiments.