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

TL;DR

This paper establishes universal bounds and thresholds for the probability of work and heat fluctuations in steady-state heat engines, extending martingale theory to non-equilibrium systems and validating results with numerical simulations.

Contribution

It introduces universal bounds for stochastic work and heat in steady-state engines and extends martingale theory to entropy production in non-equilibrium stationary states.

Findings

Universal bounds for finite-time survival probabilities.

Threshold estimates based on large deviation functions.

Validation through numerical simulations of a stochastic device.

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.