Integral equations for radial distribution functions of multicomponent mixtures on the basis of phase space scaling transformation

Scaling transformation of the phase space of a mixture component is shown to correspond to a density virtual variation of the component of a thermodynamic system. The obtained results are used to develop a technique of constructing different kinds of the generating functional to produce systems of integral equations for mixtures radial distribution functions. Empirical Tayt's equation is as well as a system of integral equations for radial distribution functions are obtained. The well-known Percus–Yevic equation and systems of equations of hypernetted chains follow from the latter equations.