Buch, Englisch, 150 Seiten, PB, Format (B × H): 170 mm x 240 mm
Buch, Englisch, 150 Seiten, PB, Format (B × H): 170 mm x 240 mm
Reihe: Zurich Lectures in Advanced Mathematics
ISBN: 978-3-03719-129-3
Verlag: EMS Press
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.
Zielgruppe
Graduate students, researchers
