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Variational Methods in Statistical Thermodynamics—A Pedagogical Introduction

Wang, Zhen-Gang (2016) Variational Methods in Statistical Thermodynamics—A Pedagogical Introduction. In: Variational Methods in Molecular Modeling. Springer , Singapore, pp. 1-29. ISBN 978-981-10-2500-6. http://resolver.caltech.edu/CaltechAUTHORS:20170711-101657842

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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.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://dx.doi.org/10.1007/978-981-10-2502-0_1DOIArticle
https://link.springer.com/chapter/10.1007%2F978-981-10-2502-0_1PublisherArticle
ORCID:
AuthorORCID
Wang, Zhen-Gang0000-0002-3361-6114
Additional Information:© 2017 Springer Science+Business Media Singapore. First Online: 18 December 2016.
Record Number:CaltechAUTHORS:20170711-101657842
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170711-101657842
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78935
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:11 Jul 2017 21:59
Last Modified:11 Jul 2017 21:59

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