Derivation of the Boltzmann equation: hard spheres, short-range potentials and beyond

TL;DR

This paper reviews the derivation of the Boltzmann equation from classical Hamiltonian dynamics, focusing on hard spheres and short-range potentials, highlighting key results and recent developments in the field.

Contribution

It synthesizes foundational and recent results on deriving the Boltzmann equation from many-body dynamics, emphasizing the role of hard spheres and short-range interactions.

Findings

Discussion of Lanford's theorem and its implications

Overview of recent advances in derivations beyond hard spheres

Clarification of conditions under which the Boltzmann equation is valid

Abstract

We review some results concerning the derivation of the Boltzmann equation starting from the many-body classical Hamiltonian dynamics. In particular, the celebrated paper by O. E. Lanford III and the more recent papers [13, 23] are discussed.