The theory of large deviations: from Boltzmann's 1877 calculation to equilibrium macrostates in 2D turbulence

Authors

RS Ellis, University of Massachusetts - AmherstFollow

Publication Date

1999

Journal or Book Title

PHYSICA D-NONLINEAR PHENOMENA

Abstract

After presenting some basic ideas in the theory of large deviations, this paper applies the theory to a number of problems in statistical mechanics. These include deriving the form of the Gibbs state for a discrete ideal gas; describing probabilistically the phase transition in the Curie–Weiss model of a ferromagnet; and deriving variational formulas that describe the equilibrium macrostates in models of two-dimensional turbulence. A general approach to the large deviation analysis of models in statistical mechanics is also formulated.

Comments

The published version is located at http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVK-3XG1SXG-8&_user=1516330&_coverDate=09%2F10%2F1999&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1699836804&_rerunOrigin=google&_acct=C000053443&_version=1&_urlVersion=0&_userid=1516330&md5=2f58f77a435d9bfb316bbdb98f914dcd&searchtype=a

Pages

106-136

Volume

133

Issue

1-4

Recommended Citation

Ellis, RS, "The theory of large deviations: from Boltzmann's 1877 calculation to equilibrium macrostates in 2D turbulence" (1999). PHYSICA D-NONLINEAR PHENOMENA. 338.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/338