  Recently, it was shown that a theoretical description of nucleation based on
fluctuating hydrodynamics and classical density functional theory can be used
to determine non-classical nucleation pathways for crystallization (Lutsko,
Sci. Adv. 5, eaav7399 (2019)). The advantage of the approach is that it is free
of any assumptions regarding order parameters and that requires no input other
than molecular interaction potentials. We now extend this fundamental framework
so as to describe the dynamics of non-classical nucleation. We use it to study
the nucleation of both droplets and crystalline solids from a low-concentration
solution of colloidal particles using two different interaction potentials. We
find that the nucleation pathways of both droplets and crystals are remarkably
similar at the early stages of nucleation until they diverge due to a rapid
ordering along the solid pathways in line with the paradigm of "non-classical"
crystallization. We compute the unstable modes at the critical clusters and
find that despite the non-classical nature of solid nucleation, the size of the
nucleating clusters remains the principle order parameter in all cases
supporting a "classical" description of the {\it dynamics} of crystallization.
We show that nucleation rates can be extracted from our formalism in a
systematic way. Our results suggest that in some cases, despite the
non-classical nature of the nucleation pathways, classical nucleation theory
can give reasonable results for solids but that there are circumstances where
it may fail. This contributes a nuanced perspective to recent experimental and
simulation work suggesting that important aspects of crystal nucleation can be
described within a classical framework.
