Maximum entropy formulation of the Kirkwood superposition approximation

The Kirkwood superposition approximation for systems at equilibrium in the thermodynamic limit was derived using a variational formulation. The entropy of the triplet correlation function was defined and it was shown that the Kirkwood closure brings the entropy to its maximal value. It was shown that this approach leads to a different interpretation for the Kirkwood closure relation, usually explained by probabilistic considerations of dependence and interdependence of particles. A variational approach was used to find closure relations for high order correlation functions.