Related papers: Perspectives in Statistical Mechanics
Gibbs measures are the main object of study in equilibrium statistical mechanics, and are used in many other contexts, including dynamical systems and ergodic theory, and spatial statistics. However, in a large number of natural instances…
Many problems of interest in computer science and information theory can be phrased in terms of a probability distribution over discrete variables associated to the vertices of a large (but finite) sparse graph. In recent years,…
We present and discuss a list of some interesting points that are currently open in nonextensive statistical mechanics. Their analytical, numerical, experimental or observational advancement would naturally be very welcome.
Although not as wide, and popular, as that of quantum mechanics, the investigation of fundamental aspects of statistical mechanics constitutes an important research field in the building of modern physics. Besides the interest for itself,…
The statistical mechanics of Gibbs is a juxtaposition of subjective, probabilistic ideas on the one hand and objective, mechanical ideas on the other. In this paper, we follow the path set out by Jaynes, including elements added…
There is no compelling reason imposing that the methods of statistical mechanics should be restricted to the dynamical systems which follow the usual Boltzmann-Gibbs prescriptions. More specifically, ubiquitous natural and artificial…
Statistical physics has proven to be a very fruitful framework to describe phenomena outside the realm of traditional physics. The last years have witnessed the attempt by physicists to study collective phenomena emerging from the…
Statistical mechanics can only be ultimately justified in terms of microscopic dynamics (classical, quantum, relativistic, or any other). It is known that Boltzmann-Gibbs statistics is based on the hypothesis of exponential sensitivity to…
In this document, we aim to gather various results related to a compositional/categorical approach to rigorous Statistical Mechanics. Rigorous Statistical Mechanics is centered on the mathematical study of statistical systems. Central…
Statistical mechanics of the discrete nonlinear Schr\"odinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for…
Our goal is to present the basic results on one-dimensional Gibbs and equilibrium states viewed as special invariant measures on symbolic dynamical systems, and then to describe without technicalities a sample of results they allowed to…
Gibbsian statistical mechanics is extended into the domain of non-negligible {though non-specified} correlations in phase space while respecting the fundamental laws of thermodynamics. The appropriate Gibbsian probability distribution is…
This is an extensive review of recent work on the foundations of statistical mechanics. Subject matters discussed include: interpretation of probability, typicality, recurrence, reversibility, ergodicity, mixing, coarse graining, past…
We briefly review Boltzmann-Gibbs and nonextensive statistical mechanics as well as their connections with Fokker-Planck equations and with existing central limit theorems. We then provide some hints that might pave the road to the proof of…
J. Willard Gibbs' Elementary Principles in Statistical Mechanics was the definitive work of one of America's greatest physicists. Gibbs' book on statistical mechanics establishes the basic principles and fundamental results that have…
At an elementary level, we present some non-perturbative aspects of non-abelian gauge theories in four dimensional space-time. Some rigorous results have been obtained in the framework of supersymmetric theories, and a very rich physics…
Statistical mechanics is one of the most powerful and elegant tools in the quantitative sciences. One key virtue of statistical mechanics is that it is designed to examine large systems with many interacting degrees of freedom, providing a…
When dealing with certain kind of complex phenomena the theoretician may face some difficulties -- typically a failure to have access to information for properly characterize the system -- for applying the full power of the standard…
An unified thermodynamical framework based in the use of a generalized Massieu-Planck thermodynamic potential is proposed and a new formulation of Boltzmann-Gibbs Statistical Mechanics is established. Under this philosophy a generalization…
A critical examination of some basic conceptual issues in classical statistical mechanics is attempted, with a view to understanding the origins, structure and statuts of that discipline. Due attention is given to the interplay between…