  We study many-party correlations quantified in terms of the Umegaki relative
entropy (divergence) from a Gibbs family known as a hierarchical model. We
derive these quantities from the maximum-entropy principle which was used
earlier to define the closely related irreducible correlation. We point out
differences between quantum states and probability vectors which exist in
hierarchical models, in the divergence from a hierarchical model and in local
maximizers of this divergence. The differences are, respectively, missing
factorization, discontinuity and reduction of uncertainty. We discuss global
maximizers of the mutual information of separable qubit states.
