Stochastic thermodynamics of resetting with imperfections

Over the past decade, stochastic processes with resetting has gained increased attention. Not only has resetting been shown to be of relevance to a myriad of systems, like extreme events in ecology and search processes, but it also facilitates the study of non-equilibrium steady states that are analytically attainable. Despite the wide range of relevancy to non-equilibrium systems, the thermodynamics of stochastic resetting is not yet fully understood. Fully developing stochastic thermodynamics for systems undergoing resetting has been difficult, as conventional resetting breaks microreversibility; time-reversed trajectories have vanishing probability. Two approaches that circumvent this issue are discussed. By allowing errors in the instantaneous resetting, time-reversed trajectories become well-defined. The full distribution of the entropy production is obtained in this case, which takes a large deviation form. Interesting phenomena like a condensation transition is discussed for certain resetting schemes. An alternate approach is to dynamically realize the resetting process over finite time, for example through switching on and off attractive potentials. Exact entropy production is derived for a large class of switching statistics, and the results are compared with that of instantaneous resetting with errors.