to the nonfreeness of the state from which it is derived [@GottliebMauser2007]. Also, nonfreeness is additive over independent subsystems: when a many-fermion state is a product of statistically independent substates, its nonfreeness is the sum of its substates’ nonfreeness [@GottliebMauser2007].

The monotonicity and additivity properties of nonfreeness derive from its definition as a relative entropy. Correlation functionals closely related to nonfreeness can be defined using Rényi divergences instead of relative entropy. Rényi divergences also enjoy the properties of additivity and monotonicity, and so do the correlation functionals defined in terms of them. Indeed, the “new measure of electron correlation" that we proposed in Ref. [@GottliebMauser2005] is of this type. However, within this class of correlation functionals, the nonfreeness functional has a couple of additional attractive properties, presently to be stated precisely.

Suppose $\Delta$ is a density operator on a fermion Fock space that represents a state of finite average particle number, and let $\Gamma_\Delta$ denote the density operator of the unique free state with the same $1$-pdm as $\Delta$. The nonfreeness of $\Delta$, or of the state it represents, is defined to be $S(\Delta \|\Gamma_\Delta)$, the entropy of $\Delta$ relative to $\Gamma_\Delta$.

The nonfreeness of $\Delta$ is given by the 