Abstract
We investigate the possibility of describing fluctuational decay of a metastable phase macroscopically, without a detailed knowledge of the microscopic kinetics. Using the ideas of microscopic reversibility, we construct a hydrodynamic-type equation which describes the buildup of fluctuations in the region of subcritical sizes. An equation of Ornstein-Uhlenbeck type is used to bridge this equation with the one describing unstable growth of larger (overcritical) fluctuations. An explicit time-dependent solution to the proposed system of equations is derived in the spirit of the singular perturbation technique. It is shown that this solution also accurately approximates the solution of the Farkas-Becker-Döring master equation, so that the macroscopic level of description is consistent with the underlying models.
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Shneidman, V.A., Hänggi, P. Microscopic reversibility and the nonlinear Einstein-Onsager relation in macroscopic description of nucleation. J Stat Phys 78, 431–439 (1995). https://doi.org/10.1007/BF02183357
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DOI: https://doi.org/10.1007/BF02183357