Waiting for rare entropic fluctuations
1 Department of Physics, Keio University - Yokohama 223–8522, Japan
2 International centre for theoretical sciences, TIFR - Bangalore 560089, India
Received: 24 February 2016
Accepted: 6 June 2016
Nonequilibrium 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 probability distributions for entropic fluctuations of various sizes to occur in a fixed time interval. An important and natural question is to ask for the time one has to wait to see fluctuations of a desired size. We address this question by studying the first-passage time distribution (FPTD). We derive the general basic equation to get the FPTD for entropic variables. Based on this, the FPTD on entropy production in a driven colloidal particle in the ring geometry is illustrated. A general asymptotic form of the FPTD and integral fluctuation relation symmetry in terms of the first passages are found.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.40.Jc – Brownian motion / 05.70.Ln – Nonequilibrium and irreversible thermodynamics
© EPLA, 2016