Nearest-neighbor distributions in fluid systems

Because nearest-neighbor probability distributions have been found to be useful for an exact investigation of the statistical thermodynamics of classical fluids, their exact form (valid for fluids in which many-body interaction potentials may obtain) has therefore been developed in the present paper. For an introductory familiarization with nearest-neighbor probability density functions (NNPDF’s) their connection with the commonly employed n-body distribution functions is first given. The usefulness of NNPDF’s in the analysis of structure in classical systems is also briefly discussed. A notable development associated with the paper is the fact that while ‘‘useful’’ exact expressions are not easily determined directly for n-body distribution functions (as evidenced by the several unsuccessful attempts to derive them in the literature), they are readily obtained directly for NNPDF’s (which are closely related functions) even where the ‘‘most general’’ interparticle interaction potentials may be said to obtain.