TY  - BOOK
AU  - Gallagher,Isabelle
AU  - Gallagher,Isabelle
AU  - Saint-Raymond,Laure
AU  - Texier,Benjamin
TI  - From Newton to Boltzmann: Hard Spheres and Short-range Potentials
T2  - Zurich Lectures in Advanced Mathematics (ZLAM)
SN  - 9783037196298
PY  - 2014///
CY  - Zuerich, Switzerland
PB  - European Mathematical Society Publishing House
KW  - Differential equations
KW  - bicssc
KW  - Partial differential equations
KW  - msc
N1  - Restricted to subscribers
N2  - 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
UR  - https://doi.org/10.4171/129
UR  - http://www.ems-ph.org/img/books/gallagher_mini.gif
ER  -