Calculation of the entropy for simple classical fluids

We consider the calculation of the excess entropy in the grand canonical ensemble and redevelop a systematic expansion in terms of the multiparticle correlation functions. The exact expansion for the entropy is written as two series of functions, one is directly related to the potentials of mean force as in the closed systems (generalizing ladder diagram expansion) and another is a sum of fluctuation corrections involving functional derivatives of potentials of mean force. The generalized superposition approximation is then applied to extract the leading contributions of the fluctuation terms as a sum of functions including both pair and triplet correlation functions (generalizing ring diagram expansion). The stationary entropy principle is used to derive two extensions of the hypernetted chain (HNC) equation for the triplet correlation function. An approximate expression of the entropy, which is suitable for numerical calculations in homogeneous systems, is also proposed.