Falsifiability test for classical nucleation theory

Classical nucleation theory (CNT) is built upon the capillarity approximation, i.e., the assumption that the nucleation properties can be inferred from the bulk properties of the melt and the crystal. Although the simplicity and usefulness of CNT cannot be overstated, experiments and simulations regularly uncover significant deviations from its predictions, which are often reconciled through phenomenological extensions of the CNT, fueling the debate over the general validity of the theory. In this Letter, we present a falsifiability test for any nucleation theory grounded in the capillarity approximation. We focus on cases where the theory predicts no differences in nucleation rates between different crystal polymorphs. We then introduce a system in which all polymorphs have the same free energy (both bulk and interfacial) across all state points. Through extensive molecular simulations, we show that the polymorphs exhibit remarkably different nucleation properties, directly contradicting predictions of CNT. We argue that CNT's primary limitation lies in its neglect of structural fluctuations within the liquid phase.