the domain of mixed many-fermion states, i.e., states that can be represented by density operators on the fermion Fock space.

A correlation functional for mixed states can be useful even if the system of interest is one of exactly $n$ fermions in a pure state, because open subsystems of the system of interest are typically in a mixed states, containing a random number of particles. Consider, for example, a system of fermions on a lattice. The fermions that occupy a given site or block of sites constitute a subsystem that is typically in a mixed state, and the von Neumann entropy of that local state can reflect physical properties such as quantum phase transitions [@VidalLatorreRicoKitaev; @GuDengLiLin; @LarssonJohannesson]. Indeed, nonfreeness has been used to quantify local correlation in a realistic tight-binding model of a transition metal oxide heterostructure [@MauserHeld]. The state of a many-fermion system determines the states of all its subsystems (e.g., local states in an extended system). The induced state of a subsystem may be called a “restriction" [@HainzlLewinSolovej] or “localization" [@LewinNamRougerie] of the state; we call it a “substate." Nonfreeness is monotone with respect to restriction of states: the nonfreeness of a substate is less than or equal 