Systematically extending classical nucleation theory

The foundation for any discussion of first order phase transitions is classical nucleation theory (CNT). CNT, developed in the first half of the twentieth century, is based on a number of heuristically plausible assumptions 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 2012 J. Chem. Phys. 136 034509) connection between CNT and fluctuating hydrodynamics. Here, this connection is described without the need for artificial assumptions such as spherical symmetry. The results are illustrated by application to CNT with moving clusters (a long-standing problem in the literature) and the construction of CNT for ellipsoidal clusters.