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It is proven that, for any soft potential characterized by a finite Fouriertransform $\widetilde{\phi}(k)$, the virial and energy thermodynamic routes areequivalent for approximations such that the Fourier transform of the totalcorrelation function divided by the density $\rho$ is an arbitrary function of$\rho\beta\widetilde{\phi}(k)$, where $\beta$ is the inverse temperature. Thisclass includes the mean spherical approximation as a particular case.Comment: 3 pages; v2: Comment on compressibility route added; to be published  in JC

Thermodynamic consistency between the energy and virial routes in the mean spherical approximation for soft potentials