  It is shown that diffusion-limited classical nucleation theory (CNT) can be
recovered as a simple limit of the recently proposed dynamical theory of
nucleation based on fluctuating hydrodynamics (Lutsko, JCP 136, 034509 (2012)).
The same framework is also used to construct a more realistic theory in which
clusters have finite interfacial width. When applied to the dilute
solution/dense solution transition in globular proteins, it is found that the
extension gives corrections to the the nucleation rate even for the case of
small supersaturations due to changes in the monomer distribution function and
to the excess free energy. It is also found that the monomer
attachement/detachment picture breaks down at high supersaturations
corresponding to clusters smaller than about 100 molecules. The results also
confirm the usual assumption that most important corrections to CNT can be
acheived by means of improved estimates of the free energy barrier. The theory
also illustrates two topics that have received considerable attention in the
recent literature on nucleation: the importance sub-dominant corrections to the
capillary model for the free energy and of the correct choice of the reaction
coordinate.
