pointed out that the minimizer is $\Gamma_{\Delta}$, and and argued that (\[minimum property\]) means that other choices of $\Gamma$ necessarily overestimate correlation. In this review we will present a very thorough proof of (\[minimum property\]).

$$\star$$

The rest of this article is organized as follows:

Section \[Density operators on Fock space\] presents the notation and terminology required for reading Sections \[Free states\] - \[Special properties of nonfreeness\].

In Section \[Free states\] we define free states. Prop. \[free at last\] there asserts that free states are substates of Slater determinant states or limits of such states.

In Section \[Relative entropy correlation functionals\] we discuss correlation functionals that are closely related to nonfreeness, focusing on properties they share.

In Section \[Special properties of nonfreeness\] we review special properties of nonfreeness. The simple formula (\[simple formula\]) for nonfreeness is developed in Prop. \[max ent prop\] and its corollary; and the minimum property (\[minimum property\]) of nonfreeness is proven in Prop. \[superproposition\].

In order not to impede the review while keeping the article as a whole fairly self-contained, many of the technical details and some of the proofs have been removed to Section \[Appendices\], which effectively consists of nine appendices.

Density operators on Fock 