Similarity of extremely rare nonequilibrium processes to equilibrium processes

For system coupled to heat baths, typical nonequilibrated processes, e.g., induced by varying an external parameter without waiting for equilibration in between, are very different from the corresponding equilibrium infinitely slow processes. Nevertheless, there are connections between equilibrium and nonequilibrated behaviors, e.g., the theorems of Jarzynski and Crooks, which relate the distribution P(W) of nonequilibrium work to the free energy differences ΔF. Here we study the naturally arising question, whether those relevant but rare trajectories, which exhibit these work values, show a higher degree of similarity to equilibrium. For convenience, we have chosen a simple model of RNA secondary structures (or single-stranded DNA), here modeling a medium-size hairpin structure, under influence of a varying external force. This allows us to measure the work W during the resulting fast unfolding and refolding processes within Monte Carlo simulations, i.e., in nonequilibrium. Also we sample numerically efficiently directly in exact equilibrium, for comparison. Using a sophisticated large-deviation algorithm, we are able to measure work distributions with high precision down to probabilities as small as 10^{-46}, enabling us to verify the Crooks and Jarzynski theorems. Furthermore, we analyze force-extension curves and the configurations of the secondary structures during unfolding and refolding for typical equilibrium processes and nonequilibrated processes. We find that the nonequilibrated processes where the work values are close to those which are most relevant for applying Crooks and Jarzynski theorems, respectively, but which occur with exponential small probabilities, are most and quite similar to the equilibrium processes.