Abstract

Events in mesoscopic processes often take place at random times. Take for instance the example of a colloidal particle escaping from a metastable state. An interesting question is how much work an external agent has exerted on the particle when it escapes the metastable state. In order to address this question, we develop a thermodynamics theory for events that take place at random times. To this aim, we apply the theory of stochastic thermodynamics, which is a thermodynamics theory for mesoscopic systems, to ensembles of trajectories terminating at random times. Using results from martingale theory, we obtain a thermodynamic bound, reminiscent of the second law of thermodynamics, for the work exerted by an external protocol on a mesoscopic system at random times.