Nonequilibrium Acceleration and Time Forecasting of Cluster-Mediated Self-Assembly.

Nonequilibrium driving accelerates self-assembly by breaking the trade-off between thermodynamic stability and kinetic accessibility. While this principle has inspired a variety of theoretical and computational approaches, its effectiveness and predictability within physically realistic simulation frameworks remain to be systematically explored. Here, we investigate its impact using the Virtual-Move Monte Carlo (VMMC) method, a widely adopted approach for simulating collective particle dynamics during self-assembly. We investigate when such acceleration is both effective and predictable for three models, namely, VMMC with directed specific interactions, VMMC with undirected specific interactions, and an undirected single-particle Monte Carlo (SPMC), serving as a benchmark. Across all cases, nonequilibrium driving significantly reduces the time to first assembly, underscoring its robustness as a strategy for improving assembly efficiency. We further assess the Stochastic Landscape Method (SLM) as a forecasting tool for these models, and find its predictive power depends strongly on the nature of the interactions. Specifically, while SPMC and VMMC with undirected interaction show similar predictability, VMMC systems with directed interactions are more predictive than undirected dynamics. Analysis of simulation energy trajectories reveals the physical basis of these differences and delineates the conditions under which predictive tools like SLM are most effective. Our results highlight nonequilibrium driving as a powerful strategy for improving complex self-assembly outcomes and identify directed binding as a key principle for enhancing predictability.