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From Newton to Boltzmann: Hard Spher...

Gallagher, Isabelle,

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From Newton to Boltzmann: Hard Spheres and Short-range Potentials

Record Type:	Electronic resources : Monograph/item
Title/Author:	From Newton to Boltzmann: Hard Spheres and Short-range Potentials/ Isabelle Gallagher, Laure Saint-Raymond, Benjamin Texier
Author:	Gallagher, Isabelle,
other author:	Saint-Raymond, Laure,
Published:	Zuerich, Switzerland :European Mathematical Society Publishing House, : 2014,
Description:	1 online resource (148 pages)
Subject:	Differential equations -
Online resource:	https://doi.org/10.4171/129
Online resource:	https://www.ems-ph.org/img/books/gallagher_mini.gif
ISBN:	9783037196298

From Newton to Boltzmann: Hard Spheres and Short-range Potentials
Gallagher, Isabelle,

From Newton to Boltzmann: Hard Spheres and Short-range Potentials[electronic resource] /Isabelle Gallagher, Laure Saint-Raymond, Benjamin Texier - Zuerich, Switzerland :European Mathematical Society Publishing House,2014 - 1 online resource (148 pages) - Zurich Lectures in Advanced Mathematics (ZLAM).

Restricted to subscribers:https://www.ems-ph.org/ebooks.php

The question addressed in this monograph is the relationship between the time-reversible Newton dynamics for a system of particles interacting via elastic collisions, and the irreversible Boltzmann dynamics which gives a statistical description of the collision mechanism. Two types of elastic collisions are considered: hard spheres, and compactly supported potentials.. Following the steps suggested by Lanford in 1974, we describe the transition from Newton to Boltzmann by proving a rigorous convergence result in short time, as the number of particles tends to infinity and their size simultaneously goes to zero, in the Boltzmann-Grad scaling. Boltzmann's kinetic theory rests on the assumption that particle independence is propagated by the dynamics. This assumption is central to the issue of appearance of irreversibility. For finite numbers of particles, correlations are generated by collisions. The convergence proof establishes that for initially independent configurations, independence is statistically recovered in the limit. This book is intended for mathematicians working in the fields of partial differential equations and mathematical physics, and is accessible to graduate students with a background in analysis.

ISBN: 9783037196298

Standard No.: 10.4171/129doiSubjects--Topical Terms:

704075
Differential equations

From Newton to Boltzmann: Hard Spheres and Short-range Potentials
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520 $a The question addressed in this monograph is the relationship between the time-reversible Newton dynamics for a system of particles interacting via elastic collisions, and the irreversible Boltzmann dynamics which gives a statistical description of the collision mechanism. Two types of elastic collisions are considered: hard spheres, and compactly supported potentials.. Following the steps suggested by Lanford in 1974, we describe the transition from Newton to Boltzmann by proving a rigorous convergence result in short time, as the number of particles tends to infinity and their size simultaneously goes to zero, in the Boltzmann-Grad scaling. Boltzmann's kinetic theory rests on the assumption that particle independence is propagated by the dynamics. This assumption is central to the issue of appearance of irreversibility. For finite numbers of particles, correlations are generated by collisions. The convergence proof establishes that for initially independent configurations, independence is statistically recovered in the limit. This book is intended for mathematicians working in the fields of partial differential equations and mathematical physics, and is accessible to graduate students with a background in analysis.
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