Equilibration and thermalization of classical systems

Numerical evidence is presented that the canonical distribution for a subsystem of a closed classical system of a ring of coupled harmonic oscillators (integrable system) or magnetic moments (nonintegrable system) follows directly from the solution of the time-reversible Newtonian equation of motion in which the total energy is strictly conserved. Without performing ensemble averaging or introducing fictitious thermostats, it is shown that this observation holds 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