Deriving integral equations for radial distribution functions of multicomponent mixtures on the basis of scale transformations in the phase space

It is shown that scale transformations of the coordinate part of the phase space for one of the mixture components correspond to virtual variations in the local density for the same component in a thermodynamic system. The investigation results are used to construct different variants of a generating functional with the goal of deriving a system of integral equations for the radial distribution functions of mixtures. An equation of state, which is a modification of the Tate equation, is obtained. Systems of integral equations that imply, in the limit, the Perkus-Yevick equations and systems of equations for hypernetted chains are derived for radial distribution functions. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 111, No. 3, pp. 473–482, June, 1997.