Titre :

A Rigourous Demonstration of the Validity of Boltzmann’s Scenario for the Spatial Homogenization of a Freely Expanding Gas and the Equilibration of the Kac Ring

Auteur(s) :

De Bievre, Stephan [Auteur]
Méthodes quantitatives pour les modèles aléatoires de la physique [MEPHYSTO-POST]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Parris, Paul [Auteur]
Missouri University of Science and Technology [Missouri S&T]

Titre de la revue :

Journal of Statistical Physics

Pagination :

772 - 793

Éditeur :

Springer Verlag

Date de publication :

2017-08

ISSN :

0022-4715

Discipline(s) HAL :

Physique [physics]/Physique mathématique [math-ph]
Mathématiques [math]

Résumé en anglais : [en]

Boltzmann provided a scenario to explain why individual macroscopic systems composed of a large number $N$ of microscopic constituents are inevitably (i.e., with overwhelming probability) observed to approach a unique ...
Lire la suite >Boltzmann provided a scenario to explain why individual macroscopic systems composed of a large number $N$ of microscopic constituents are inevitably (i.e., with overwhelming probability) observed to approach a unique macroscopic state of thermodynamic equilibrium, and why after having done so, they are then observed to remain in that state, apparently forever. We provide here rigourous new results that mathematically prove the basic features of Boltzmann’s scenario for two classical models: a simple boundary-free model for the spatial homogenization of a non-interacting gas of point particles, and the well-known Kac ring model. Our results, based on concentration inequalities that go back to Hoeffding, and which focus on the typical behavior of individual macroscopic systems, improve upon previous results by providing estimates, exponential in $N$, of probabilities and time scales involved.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet ANR :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL