Survival and extreme statistics of work, heat, and entropy production in steady-state heat engines

Abstract

We derive universal bounds for the finite-time survival probability of the stochastic work extracted in steady-state heat engines and the stochastic heat dissipated to the environment. We also find estimates for the time-dependent thresholds that these quantities does not surpass with a prescribed probability. At long times, the tightest thresholds are proportional to the large deviation functions of stochastic entropy production. Our results entail an extension of martingale theory for entropy production, for which we derive universal inequalities involving its maximum and minimum statistics that are valid for generic Markovian dynamics in non-equilibrium stationary states. We test our main results with numerical simulations of a stochastic photoelectric device.

5+4 pages; 3+1 figures. v2: 6+4 pages, 3+2 figures (format changed, presentation improved, extra figure). Accepted in Phys. Rev. E

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Cited by in corpus (8)

• Martingales for physicists: A treatise on stochastic thermodynamics and beyond
• Thermodynamics of computations with absolute irreversibility, unidirectional transitions, and stochastic computation times
• Extreme value statistics of edge currents in Markov jump processes and their use for entropy production estimation
• Conditional fluctuation theorems and entropy production for monitored quantum systems under imperfect detection
• Gambling Carnot Engine
• Work statistics at first-passage times
• Thermodynamic inference in molecular motors: a Martingale approach
• Stochastic dynamics from maximum entropy in action space