A selective review of methods of statistical mechanics

Kristopher A. Innanen

Elsewhere in this report we make some suggestions about the use of statistical - mechanical models to assess geophysical inverse problems. Computational difficulties appear in general when the Boltzmann theory is applied to real-world problems, with only a relatively small number of problems giving rise to summable series and closed-form solutions. So, our approach has been to start from well-known models that have been shown to be mathematically tractable, and press these into geophysical service. (If this proves to be a valuable exercise, expending the resources to solve more computationally involved versions may then be justifiable.) In this review, we set up some of the ideas and concepts of statistical mechanics, as well as the basics from which we establish and analyze models. Then, we review several relevant models, some with the aim of exemplifying the rules, and others because of their possible use in geophysics. The latter class includes especially (or so it seems at present) the molecular zipper and the law of atmospheres.