A General Algorithm for Sampling Rare Events in Non-Equilibrium and Non-Stationary Systems

Although many computational methods for rare event sampling exist, this type of calculation is not usually practical for general nonequilibrium conditions, with macroscopically irreversible dynamics and 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 the parallel open asymmetric exclusion process (p-o ASEP). 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.

💡 Research Summary

The paper introduces a versatile algorithm for sampling rare events in systems that are both non‑equilibrium and non‑stationary, addressing a long‑standing limitation of existing rare‑event methods which typically require either equilibrium conditions, metastable states, or prior knowledge of the dominant reaction pathways. The core idea is to discretize the full phase space of the system into a collection of “cells” (or sub‑regions) and to treat the dynamics as a time‑dependent Markov chain on this coarse‑grained space. Unlike traditional transition‑path sampling, forward‑flux sampling, or weighted‑ensemble techniques, the proposed method does not assume a fixed transition network; instead, it builds and continuously updates a transition matrix (P_{ij}(t)) that captures the probability of moving from cell (i) to cell (j) during a short time interval (