Relaxation of an Isolated Ensemble of Harmonic Oscillators

Abstract

The collisional relaxation of an isolated ensemble of harmonic oscillators (at constant volume and energy) from initial nonequilibrium distributions is discussed in this paper. The ``transport equation'' for the relaxation process is derived and it is shown that it can be linearized even though the relaxation takes place via binary oscillator collisions. The final, stationary distribution is found to be a Boltzmann one with a temperature uniquely defined by the mean energy of the ensemble. The Boltzmann H function is obtained for this system of relaxing oscillators and it is shown that dH/dtt. The time rate of change of the mean‐square deviation of the energy during the relaxation process is computed and is shown to be closely related to the time variation of the mean energy in the relaxation of an ensemble of harmonic oscillators in contact with a thermal reservoir.