scispace - formally typeset
Open AccessBook

Statistical Mechanics: Rigorous Results

David Ruelle
Reads0
Chats0
TLDR
The problem of phase transition group invariance of physical states has been studied in the literature as discussed by the authors, where the thermodynamic limit for thermodynamic functions has been investigated in the context of statistical mechanics.
Abstract
Thermodynamic behaviour - ensembles the thermodynamic limit for thermodynamic functions - lattice systems the thermodynamic limit for thermodynamic functions - continuous systems low density expansions and correlation functions the problem of phase transitions group invariance of physical states the states of statistical mechanics Appendix: some mathematical tools

read more

Citations
More filters
BookDOI

Equilibrium states and the ergodic theory of Anosov diffeomorphisms

Rufus Bowen
TL;DR: Gibbs Measures and Gibbs measures have been used in this article to define Axiom a Diffeomorphisms for general Thermodynamic Formalism and Ergodic Theory of Axiom-a-Diffeomorphism.
Journal ArticleDOI

The large deviation approach to statistical mechanics

TL;DR: The theory of large deviations as mentioned in this paper is concerned with the exponential decay of probabilities of large fluctuations in random systems, and it provides exponential-order estimates of probabilities that refine and generalize Einstein's theory of fluctuations.
Book

An Introduction to Random Matrices

TL;DR: The theory of random matrices plays an important role in many areas of pure mathematics and employs a variety of sophisticated mathematical tools (analytical, probabilistic and combinatorial) as mentioned in this paper.
Journal ArticleDOI

Fractional quantum mechanics and Lévy path integrals

TL;DR: In this article, a new extension of a fractality concept in quantum physics has been developed and path integrals over the Levy paths are defined and fractional quantum and statistical mechanics have been developed via new fractional path integral approach.
Journal ArticleDOI

The large deviation approach to statistical mechanics

TL;DR: The theory of large deviations as discussed by the authors is concerned with the exponential decay of probabilities of large fluctuations in random systems, and it provides exponential-order estimates of probabilities that refine and generalize Einstein's theory of fluctuations.