Planck-like Distributions in Classical Nonlinear Mechanics

The classical equations of motion for a finite chain of particles with a nearest-neighbor Lennard-Jones interaction are solved numerically and, for a broad class of initial conditions, Planck-like distributions are obtained for the time averages of the energies of the normal modes. For physical values of the parameters in the problem, the action constant entering such a distribution turns out to be of the order of magnitude of Planck's constant.