High-order compressibility integrals in classical fluids

The normalization condition of the 3- and 4-particle distribution functions is used to integrate the closure relations that generalize the well-known Ornstein-Zernike (OZ) integral for the compressibility and the two-particle correlation. In a similar way to the two-body OZ relation, the 3- and 4-particle closure integrals are written in terms of the compressibility and its derivatives, allowing their immediate evaluation. These explicit expressions are useful in the perturbation theory of fluids and in testing approximations for the 3- and 4-particle correlations, such as Kirkwood's superposition approximation. As an illustration, these closure integrals are evaluated for the hard-sphere system. (Author)