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

## TL;DR

Nonequilibrium driving speeds up self-assembly processes and can be predicted using specific methods depending on the type of interactions involved.

## Contribution

The study systematically evaluates nonequilibrium driving's effectiveness and predictability in self-assembly simulations using different models.

## Key findings

- Nonequilibrium driving significantly reduces the time to first assembly across multiple models.
- Predictability of assembly time depends strongly on the nature of particle interactions.
- Directed interactions in VMMC systems enhance predictability compared to undirected dynamics.

## Abstract

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.