Title :

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

Author(s) :

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

Journal title :

Journal of Statistical Physics

Pages :

772 - 793

Publisher :

Springer Verlag

Publication date :

2017-08

ISSN :

0022-4715

HAL domain(s) :

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

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL