Variational Methods in Statistical Thermodynamics—A Pedagogical Introduction
- Creators
-
Wang, Zhen-Gang
- Other:
- Wu, Jianzhong
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.
Additional Information
© 2017 Springer Science+Business Media Singapore. First Online: 18 December 2016.Additional details
- Eprint ID
- 78935
- Resolver ID
- CaltechAUTHORS:20170711-101657842
- Created
-
2017-07-11Created from EPrint's datestamp field
- Updated
-
2021-11-15Created from EPrint's last_modified field