---
abstract: |
    This article is a brief review of “nonfreeness" and related measures of “correlation" for many-fermion systems.

    The many-fermion states we deem “uncorrelated" are the gauge-invariant quasi-free states. Uncorrelated states of systems of finitely many fermions we call simply “free" states. Slater determinant states are free; all other free states are “substates" of Slater determinant states or limits of such.

    The nonfreeness of a many-fermion state equals the minimum of its entropy relative to all free states. Correlation functionals closely related to nonfreeness can be defined in terms of Rényi entropies; nonfreeness is the one that uses Shannon entropy. These correlation functionals all share desirable additivity and monotonicity properties, but nonfreeness has some additional attractive properties.
author:
- 'Alex D. Gottlieb[^1]  and Norbert J. Mauser'
title: 'Nonfreeness and related functionals for measuring correlation in many-fermion states'
---

Introduction
============

“Nonfreeness" is an entropy functional of states of many-electron systems. It was introduced as a “measure of electron correlation" [@GottliebMauser2007; @GottliebMauserArchived] that is purely a functional of the many-electron state, depending only on the structure of the state and not upon the physical circumstances attending it, e.g., the Hamiltonian operator for the system [@correlation].

By definition, the nonfreeness of 