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Imagine a number of particles, all confined in a parabolic potential. The particles initially have a random velocity and are let free to bounce off each other (say, it's rigid spheres). Does statistical physics say anything in the case that the total initial momentum is different than zero? In particular, does it predict any of these scenarios:

  1. the system decreases its total momentum, eventually reaching zero (e.g. no momentum conservation)
  2. the system behaves in an analogue way to an harmonic oscillator (e.g. "average" momentum conservation)
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  • $\begingroup$ To clarify, do you mean that the particles are confined in an external parabolic potential or that they interact with each other through a parabolic potential? $\endgroup$ – By Symmetry Oct 5 '16 at 16:00
  • $\begingroup$ Please elaborate on the question; are the particles enclosed in a rigid box? $\endgroup$ – Harsha Oct 5 '16 at 19:11
  • $\begingroup$ @BySymmetry clarified: it's rigid spheres in a confining parabolic potential, but I would not expect these details to matter, I just care about an overall confining potential being there. $\endgroup$ – Lorenzo Pistone Oct 5 '16 at 20:40
  • $\begingroup$ @Harsha, I didn't mention one so no there is no closed box. Just the confining potential. $\endgroup$ – Lorenzo Pistone Oct 5 '16 at 20:41
  • $\begingroup$ If the particles do not all have identical masses, I believe the center of mass will jiggle around: the average force will be determined by the average position, not the center of mass. $\endgroup$ – Nanite Oct 5 '16 at 21:09

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