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Mathematical Physics Seminar

Webinar: Izaak Neri - Using martingales to study fluctuations of currents in first-passage problems of nonequilibrium processes

Location:  Zoom
Date & time: Wednesday, 29 May 2024 at 10:45AM - 11:45PM




Izaak Neri – King’s College London

Wednesday, May 29th, 10:45AM EDT (Zoom meeting starts at 10:30 EDT) 


Using martingales to study fluctuations of currents in first-passage problems of nonequilibrium processes

With current imaging methods it is possible to measure the fluctuations of nonequilibrium mesoscopic systems, such as, molecular motors, cilia, or cell membranes.  Such systems contain fluctuating currents with nonzero average values.  A question of interest in statistical physics is how current fluctuations are related to thermodynamic quantities, such as, the rate of dissipation.   Here, we study current fluctuations from the perspective of a first-passage problem, namely, we consider the first time that a fluctuating current exits an interval of finite width.  In the specific case that the current is a one-dimensional, biased, random walk this is the gambler’s ruin problem introduced by Pascal in the 17th century, which is one of the first problems studied in probability theory.  However, in this seminar we aim to understand the gambler’s ruin problem for a generic current in an arbitrary Markov process.  To this purpose, we introduce a class of martingales associated with fluctuating currents in Markov processes.  An interesting point is that these martingales naturally relate to the theory of large deviations of the corresponding fluctuating currents, for which there has been much detailed study in statistical physics.   Using this connection we can derive several interesting universal expressions relating the fluctuations of nonequilibrium currents at first-passage times to the rate of dissipation.    


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