Entropy approximations for simple fluids

Liquid state entropy formulas based on configurational probability distributions are examined for Lennard-Jones fluids across a range temperatures and densities. These formulas are based on expansions of the entropy in a series of $n$-body distribution functions. We focus on two special cases. One, which we term the "perfect gas" series, starts with the entropy of an ideal gas; the other, which we term the "dense liquid" series, removes a many-body contribution from the ideal gas entropy and reallocates it among the subsequent $n$-body terms. We show that the perfect gas series is most accurate at low density, while the dense liquid series is most accurate at high density. We propose empirical interpolation methods that are capable of connecting the two series and giving consistent predictions in most situations.