The use of open boundaries in stochastic hydrodynamic models of nucleation

Stochastic hydrodynamics is a central tool in the study of first order phase transitions at a fundamental level. Combined with sophisticated free energy models, e.g. as developed in classical Density Functional Theory, complex processes such as crystallization can be modeled and information such as free energy barriers, nucleation pathways and the unstable eigenvector and eigenvalues determined. The latter are particularly interesting as they play key roles in defining the natural (unbiased) order parameter and the nucleation rate respectively. As is often the case, computational realities restrict the size of system that can be modeled and this makes it difficult to achieve experimental conditions for which the volume is effectively infinite. In this paper, the use of open boundary conditions is discussed. By using an open system, the calculations become much closer to experimental conditions however, the introduction of open boundary conditions raises a number of questions concerning the stochastic model such as whether the fluctuation-dissipation relation is preserved and whether stationary points on the free energy surface remain stationary points of the dynamics.