Equilibration and Thermalization of Classical Systems

TL;DR

This paper shows that the canonical distribution naturally emerges for subsystems of closed classical systems, regardless of integrability, from Newtonian dynamics with conserved energy, applicable to realistic system sizes and times.

Contribution

It proves that the canonical distribution arises directly from Newtonian mechanics for subsystems, even in small and experimentally relevant systems, without additional assumptions.

Findings

Canonical distribution follows from Newtonian dynamics with energy conservation.

Valid for both integrable and nonintegrable systems.

Applicable to systems with as few as a few thousand particles.

Abstract

It is demonstrated that the canonical distribution for a subsystem of a closed system follows directly from the solution of the time-reversible Newtonian equation of motion in which the total energy is strictly conserved. It is shown that this conclusion holds for both integrable or nonintegrable systems even though the whole system may contain as little as a few thousand particles. In other words, we demonstrate that the canonical distribution holds for subsystems of experimentally relevant sizes and observation times.