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We present an alternative derivation of the pair correlation function forsimple classical fluids by using a variational approach. That approach involvesthe conditional probability p(3,..., N /1, 2) of an undefined system of Nparticles with respect to a given pair (1,2), and the definition of aconditional entropy $\sigma$(3,..., N /1, 2). An additivity assumption of$\sigma$(3,..., N /1, 2) together with a superposition assumption for p(3 / 1,2) allows deriving the pair probability p(1,2). We then focus onto the case ofsimple classical fluids, which leads to an integral, non-linear equation thatformally allows computing the pair correlation function g(R). That equationadmits the one resulting from the hyper netted chain approximation (and thePercus-Yevick approximation) as a limit case.

Conditional entropy; an alternative derivation of the pair correlation function for simple classical fluids