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The laws of thermodynamics can be extended to mesoscopic systems for which energy changes are on the order of the thermal energy are relevant. Therefore, thermodynamic observables associated with mesoscopic degrees of freedom are stochastic. A key example of such thermodynamic observable is the stochastic entropy production in nonequilibrium processes. Little is known beyond fluctuation theorems about universal statistics of entropy-production fluctuations. Using Martingale theory we have discovered novel universal statistics of stochastic entropy production in nonequilibrium steady states such as: (i) The distribution of the negative record (which we call infimum) of entropy production (ii) the passage probabilities of entropy production; (iii) the stopping-time fluctuations of entropy production. Our work is based on the finding that in a nonequilibrium steady state, the exponential of minus the entropy production is a martingale process. A martingale is a process representing a fair game with no net gain or loss and its connection to thermodynamics has not been fully explored yet. Notably, our results have interesting implications for stochastic processes that can be discussed in colloidal systems and active molecular processes. For example, we make predictions for the distribution of the maximum backtrack depth of RNA polymerases during transcription.

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Edgar Roldan, MPI-PKS Dresden
TP seminar room 0.03
Contact: Joachim Krug