Work fluctuations and Jarzynski equality in stochastic resetting

Synopsis

Stochastic thermodynamics is a cornerstone in non-equilibrium statistical physics. The last two decades have seen an enormous volume of theoretical and experimental studies in understanding the thermodynamics of small systems, where the major effort has been in the direction of non-equilibrium fluctuations of thermodynamic observables. This gave rise to many exact relations such as fluctuation theorem, Jarzynski equality, etc.. In this talk, I will present a general formalism to characterize work fluctuations in an irreversible non-equilibrium process namely the stochastic resetting which has recently attracted considerable attention due to its paramount importance in physics, chemistry and biology.  I have divided the talk into two parts. In the first part of the talk, I will give a brief introduction to the stochastic resetting mechanism. In the second part, I will present a general theory of work fluctuations in the paradigm framework of a colloidal particle in an externally modulated potential with the aid of renewal formalism of resetting. Thus, in addition to the short range diffusive motion, the particle also experiences intermittent long jumps that reset the particle back at a preferred location. Due to the modulation of the trap, work is done on the system and we investigate the statistical properties of the work fluctuations. Two central results will be discussed. 1) We find that the distribution function of the work typically, in asymptotic times, converges to a universal Gaussian form for any protocol as long as that is also renewed after each resetting event. 2) When observed for a finite time, we show that the system does not generically obey the Jarzynski equality which connects the finite time work fluctuations to the difference in free energy. However, we show that the Jarzynski equality is always fulfilled when the protocols continue to evolve without being reset.