Sampling Rare Events in Non-Stationary Dynamics

Study of rare events such as nucleation or arrest in non-equilibrium physics is ever more fashionable, but existing rare event methods intended to enhance sampling (such as umbrella sampling and FFS) are not usually practical for general nonequilibrium conditions (away from both stationary and metastable states). A novel method for calculating the time-series of the probability of a rare event is presented which is designed for these conditions. The method is validated for the cases of the Glauber-Ising model under time-varying shear flow, the Kawasaki-Ising model after a quench into the region between nucleation dominated and spinodal decomposition dominated phase change dynamics, and also for the parallel-open asymmetric exclusion process. The method requires a subdivision of the phase space of the system: it is benchmarked and found to scale well for increasingly fine subdivisions, meaning that it can be applied without detailed foreknowledge of the physically important reaction pathways.