Waiting for rare entropic fluctuations

Abstract

Non-equilibrium fluctuations of various stochastic variables, such as work and entropy production, have been widely discussed recently in the context of large deviations, cumulants and fluctuation relations. Typically, one looks at the distribution of these observables, at large fixed time. To characterize the precise stochastic nature of the process, we here address the distribution in the time domain. In particular, we focus on the first passage time distribution (FPTD) of entropy production, in several realistic models. We find that the fluctuation relation symmetry plays a crucial role in getting the typical asymptotic behavior. Similarities and differences to the simple random walk picture are discussed. For a driven particle in the ring geometry, the mean residence time is connected to the particle current and the steady state distribution, and it leads to a fluctuation relation-like symmetry in terms of the FPTD.

5+7 pages, 3 figures

References in corpus (8)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The large deviation approach to statistical mechanics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Symmetry in Full Counting Statistics, Fluctuation Theorem, and Relations among Nonlinear Transport Coefficients in the Presence of a Magnetic Field
• The Einstein relation generalized to non-equilibrium
• Work and heat probability distribution of an optically driven Brownian particle: Theory and experiments
• Large deviations of heat flow in harmonic chains
• Efficiency of molecular machines with continuous phase space

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