  The foundation for any discussion of first-order phse transitions is
Classical Nucleation Theory(CNT). CNT, developed in the first half of the
twentieth century, is based on a number of heuristically plausible assumtptions
and the majority of theoretical work on nucleation is devoted to refining or
extending these ideas. Ideally, one would like to derive CNT from a more
fundamental description of nucleation so that its extension, development and
refinement could be developed systematically. In this paper, such a development
is described based on a previously established (Lutsko, JCP 136:034509, 2012 )
connection between Classical Nucleation Theory and fluctuating hydrodynamics.
Here, this connection is described without the need for artificial assumtions
such as spherical symmetry. The results are illustrated by application to CNT
with moving clusters (a long-standing problem in the literature) and the
constructrion of CNT for ellipsoidal clusters.
