Abstract: This chapter presents a pedagogical introduction to the variational methods in statistical thermodynamics. We start with some general considerations of the variational nature of thermodynamics, which is rooted in the second law, and manifested in the maximum-term method in the evaluation of the partition function in statistical mechanics. We present two common mathematical variational techniques, one based on the Gibbs-Bogoliubov-Feynman (GBF) variational bound and one based on the saddle-point (or steepest-descent) method. We illustrate the use of these techniques in the derivation of the mean-field theory for Ising model and the Poisson-Boltzmann equation. We also show that the GBF method provides a self-consistent treatment of fluctuation effects in weakly correlated systems.

ISSN: 2364-5083

ID: CaltechAUTHORS:20170711-101657842

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Abstract: We combine a newly developed density-functional theory with string method to calculate minimum free energy path of bubble nucleation in compressible poly(methyl methacrylate)-CO_2 mixtures. As increasing initial pressure in the vicinity of a metstable phase transition, the terminal nucleated state jumps from the branch of CO_2- rich-vapor phase to the branch of CO_2 -rich-liquid phase with a jump reduction for free energy barrier and radius of critical nucleus. This result suggests that the nucleation rate is enhanced as a jump discontinuous function of the initial pressure around the boundary of metastable phase transition.

ID: CaltechAUTHORS:20130603-102554449

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