Abstract
A system consisting of an arbitrary number of particles of equal masses interacting via an arbitrary potential of homogeneity degree −2 and confined by an isotropic harmonic potential has the property of sustaining undamped isochronous compressional oscillations, as has been shown earlier. In this paper, we review and generalize this finding, and also the concept of thermodynamic equilibrium for such systems. It turns out that these compressional oscillations are adiabatic, and that correspondingly, the temperature varies when the size of the system does (in the specific case stated above, this dependence is one of inverse proportionality). It is also shown that some of these results extend to the quantal case.
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