THERMODYNAMIC CONSISTENCY AND CLASSICAL LIQUID STRUCTURAL THEORY

For classical liquids, with density-independent pair potentials phi(r) which possess a Fourier transform, a full study is made of the Born-G reen-Yvon equation which links pair correlations, via the three-partic le correlation function g3, with the potential. It is shown that the s hape of classical liquid structural theory is thereby determined, the pair potential phi(r) being given as the difference between a function in r space involving both g3 and phi(r), and a convolution of this sa me function with the Ornstein-Zernike direct correlation function. Int o this equation, a decomposition of the direct correlation function is inserted, which is designed to retain thermodynamic consistency betwe en virial and compressibility routes to the equation of state, when ap proximations to g3 are introduced, as is presently inevitable in analy tical work. Some aspects of the procedure proposed are illustrated usi ng the example of the two-dimensional one-component plasma with an int eraction satisfying Poisson's equation in two dimensions.