02601nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084001500185100003400200245015300234260008200387300003400469336002600503337002600529338003600555347002400591490005100615506006600666520126500732650003501997650004002032700003502072700003102107856003202138856006902170173-140123CH-001817-320140123234500.0a fot ||| 0|cr nn mmmmamaa140123e20140118sz fot ||| 0|eng d a978303719629870a10.4171/1292doi ach0018173 7aPBKJ2bicssc a35-xx2msc1 aGallagher, Isabelle,eauthor.10aFrom Newton to Boltzmann: Hard Spheres and Short-range Potentialsh[electronic resource] /cIsabelle Gallagher, Laure Saint-Raymond, Benjamin Texier3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2014 a1 online resource (148 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe 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.07aDifferential equations2bicssc07aPartial differential equations2msc1 aSaint-Raymond, Laure,eauthor.1 aTexier, Benjamin,eauthor.40uhttps://doi.org/10.4171/129423cover imageuhttps://www.ems-ph.org/img/books/gallagher_mini.gif