Journal of Statistical Physics, Vol. 61, Nos. 1/2, 1990. p. 143-160.
We present a novel formalism for the generation of integral equations for the distribution functions of fluids. It is based on a cumulant expansion for the free energy. Truncation of the expansion at the Kth term and minimization of the resulting approximation leads to equations for the distribution functions up to Kth order.
The formalism is not limited to systems with two-body interactions and does not require the addition of closure relations to yield a complete set of equations. In fact, it automatically generates superposition approximations, such as the Kirkwood three-body superposition approximation or the Fisher-Kopeliovich four-body one. The conceptual approach is adapted from the cluster variation method of lattice theory.