The role of fluctuations in the nucleation process

Abstract: The emergence upon cooling of an ordered solid phase from a liquid is a remarkable example of self-assembly, which has also major practical relevance. Here, we use a recently developed committor-based enhanced sampling method [Kang et al., Nat. Comput. Sci. 4, 451-460 (2024); Trizio et al., Nat. Comput. Sci. 1-10 (2025)] to explore the crystallization transition in a Lennard-Jones fluid, using Kolmogorov's variational principle. In particular, we take advantage of the properties of our sampling method to harness a large number of configurations from the transition state ensemble. From this wealth of data, we achieve precise localization of the transition state region, revealing a nucleation pathway that deviates from idealized spherical growth assumptions. Furthermore, we take advantage of the probabilistic nature of the committor to detect and analyze the fluctuations that lead to nucleation. Our study nuances classical nucleation theory by showing that the growing nucleus has a complex structure, consisting of a solid core surrounded by an interface that is more disordered than bulk liquid. We also compute from the Kolmogorov's principle a nucleation rate that is consistent with the experimental results at variance with previous computational estimates.