Small systems have non-Maxwellian momentum distributions in the microcanonical ensemble

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Abstract
The distribution of particle momentum in the canonical ensemble has the well-known Maxwell form. In the microcanonical ensemble this is not the case and the distribution of particle momentum has a different form that approaches the Maxwell form in the thermodynamic limit. Besides their intrinsic interest, these results could be of importance in studies of small systems, such as clusters. Exact results are illustrated for rigid rods, disks, and spheres.