Second law of thermodynamics at stopping times

Abstract

Events in mesoscopic systems often take place at first-passage times, as is for instance the case for a colloidal particle that escapes a metastable state. An interesting question is how much work an external agent has done on a particle when it escapes a metastable state. We develop a thermodynamic theory for processes in mesoscopic systems that terminate at stopping times, which generalize first-passage times. This theory implies a thermodynamic bound, reminiscent of the second law of thermodynamics, for the work exerted by an external protocol on a mesoscopic system at a stopping time. As an illustration, we use this law to bound the work required to stretch a polymer to a certain length or to let a particle escape from a metastable state.

14 pages, 4 figures, the new version fixes some minor typographical errors

References in corpus (4)

• Ensemble and Trajectory Thermodynamics: A Brief Introduction
• Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables
• Fundamental Bounds on First Passage Time Fluctuations for Currents
• Quantum Martingale Theory and Entropy Production

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