Abstract
It is proven that, for any soft potential φ(r) characterized by a finite Fourier transform φ̃(k), the virial and energy thermodynamic routes are equivalent if the Fourier transform of the total correlation function divided by the density ρ, h̃(k)/ρ, is an arbitrary function of ρβφ̃(k), where β is the inverse temperature. This class of approximations includes the mean spherical approximation as a particular case.
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