Variational soft-sphere perturbation theory and conditions for a Grüneisen equation of state for dense fluids

Variational perturbation calculations with various soft inverse-power potentials as reference demonstrate that the equation of state (EOS) for a wide variety of physically conceivable pair potentials, in the strong-coupling (dense-fluid) regime, may be characterized by a universal scaled pair distribution function of the form $g(r{\rho }^{\frac{1}{3}},\frac{s^E}{N{k}_B})$. This universality, which has been already conjectured by the examination of various applications of the hard-sphere perturbation theory, is equivalent to a statement of additivity of EOS's if the density $\rho$ and the excess entropy $s^E$ serve as the independent variables. With the use of "additivity" with the inverse powers as the basis set of potentials, simple conditions for the validity of a Grüneisen-type scaling EOS are obtained, based on general features of the effective pair potential for the material.