Abstract
We consider the statistical mechanics of a system in which the particles interact through a velocity-dependent potential, of the form p ijV(| r ij|)· p ij( p ij is the relative momentum of the i th and j th particles) . The aim of the investigation is to gain further understanding of the formal relationship between velocity-dependent potentials and hard-core potentials in an explicity many-body context. In the limit of classical statistics, we find that the above interaction is indistinguishable from a hard-sphere potential; in particular the specific heat is just that for an ideal gas, a property which for velocity-independent potentials is specific to the hard-sphere case. In the limit of quantum statistics, the two potentials (velocity-dependent and hard-sphere) are no longer equivalent: it is no clear whether addition of a static potential to the velocity-dependent one could restore the exact equivalence.
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