  We present an alternative derivation of the pair correlation function for
simple classical fluids by using a variational approach. That approach involves
the conditional probability p(3,..., N /1, 2) of an undefined system of N
particles with respect to a given pair (1,2), and the definition of a
conditional 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 of
simple classical fluids, which leads to an integral, non-linear equation that
formally allows computing the pair correlation function g(R). That equation
admits the one resulting from the hyper netted chain approximation (and the
Percus-Yevick approximation) as a limit case.
