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The foundation for any discussion of first-order phse transitions isClassical Nucleation Theory(CNT). CNT, developed in the first half of thetwentieth century, is based on a number of heuristically plausible assumtptionsand the majority of theoretical work on nucleation is devoted to refining orextending these ideas. Ideally, one would like to derive CNT from a morefundamental description of nucleation so that its extension, development andrefinement could be developed systematically. In this paper, such a developmentis 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 assumtionssuch as spherical symmetry. The results are illustrated by application to CNTwith moving clusters (a long-standing problem in the literature) and theconstructrion of CNT for ellipsoidal clusters.

Systematically extending classical nucleation theory