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We derive universal bounds for the finite-time survival probability of thestochastic work extracted in steady-state heat engines and the stochastic heatdissipated to the environment. We also find estimates for the time-dependentthresholds that these quantities does not surpass with a prescribedprobability. At long times, the tightest thresholds are proportional to thelarge deviation functions of stochastic entropy production. Our results entailan extension of martingale theory for entropy production, for which we deriveuniversal inequalities involving its maximum and minimum statistics that arevalid for generic Markovian dynamics in non-equilibrium stationary states. Wetest our main results with numerical simulations of a stochastic photoelectricdevice.

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