a many-fermion state is its entropy relative to the unique gauge-invariant quasi-free state with the same $1$-particle density matrix ($1$-pdm). Gauge-invariant quasi-free (GIQF) states have $0$ nonfreeness by definition, but the nonfreeness of any other many-fermion state is positive, possibly infinite. Slater determinant states of $n$-fermions and “Fermi sea" states of infinitely many fermions are GIQF, as are restrictions of such states. Conversely, any GIQF state can be represented as restriction of a Slater determinant or Fermi sea state. These are the states we deem “uncorrelated."

In this article we shall mainly consider normal states of finite systems of fermions, identifying such states with the density operators that represent them on a fermion Fock space. Among such states we focus on those that have finite expected particle number. The GIQF states of finite average particle number we call simply “free" states.

For pure $n$-fermion states, the nonfreeness functional coincides with “particle-hole symmetric correlation entropy" [@Gori-GiorgiZiesche]. Particle-hole symmetric correlation entropy has been used to quantify electron correlation in the uniform electron gas [@Gori-GiorgiZiesche] and in short linear chains undergoing a Mott transition [@Bendazzoli...]. Particle-hole symmetric correlation entropy is defined only for pure states; nonfreeness is an extension of that functional to 