The Dominant Role of Rare Events in Out-of-Equilibrium Processes

The Jarzynski’s equality, a remarkable result in modern statistical mechanics, allows us to calculate the free energy of a system, which is a function of state defined only for equilibrium states, from an exponential average of work values resulting from a large number of realizations of a process in which the system goes through, and ends at, out-of-equilibrium states. Limitations to the applicability of this equality are mainly due to the dearth of work values corresponding to infrequent, but dominant, realizations known as rare events. Adopting a heuristic approach, we present a simple example to illustrate the relevance of rare events by analyzing the numerical results of a single-particle stochastic thermodynamic model. We discuss how the applicability of the Jarzynski’s equality depends on the number and distribution of rare events, which in turn are determined by the number of repetitions of a work process and its duration, as well as on the rate at which work is performed on the system. Data explorations similar to the one carried out here can be used to asses if free energies calculated from experimental data or more realistic models are reproducible, typical or random results.