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We investigate thermodynamics of general nonequilibrium processes stopped atstochastic times. We propose a systematic strategy for constructingfluctuation-theorem-like martingales for each thermodynamic functional,yielding a family of stopping-time fluctuation theorems. We derivesecond-law-like thermodynamic inequalities for the mean thermodynamicfunctional at stochastic stopping times, the bounds of which are stronger thanthe thermodynamic inequalities resulting from the traditional fluctuationtheorems when the stopping time is reduced to a deterministic one. Numericalverification is carried out for three well-known thermodynamic functionals,namely, entropy production, free energy dissipation and dissipative work. Theseuniversal equalities and inequalities are valid for arbitrary stoppingstrategies, and thus provide a comprehensive framework with new insights intothe fundamental principles governing nonequilibrium systems.

Fluctuation Theorems and Thermodynamic Inequalities for Nonequilibrium Processes Stopped at Stochastic Times