following simple formula, provided its von Neumann entropy $S(\Delta) = -\Tr (\Delta \log\Delta)$ is finite: $$\begin{aligned}
\label{simple formula}
\lefteqn{ S(\Delta \| \Gamma_{\Delta}) \equals  S(\Gamma_{\Delta}) - S(\Delta) }\nonumber \\
        & = &   - \sum p_j \log p_j - \sum (1-p_j) \log(1-p_j)  \ - \ S(\Delta) \qquad\end{aligned}$$ where the $p_j$ denote the eigenvalues of the $1$-pdm of $\Delta$, its natural occupation numbers.

In any case, the nonfreeness of a many-fermion state is equal to the minimum of its entropy relative to all free states: $$\label{minimum property}
 S(\Delta \|\Gamma_\Delta) \equals \min \big\{S(\Delta\|\Gamma ) : \ \Gamma  \ \hbox{is free} \big\}\ .$$ Moreover, if the minimum in (\[minimum property\]) is finite, then $\Gamma = \Gamma_\Delta$ is the unique minimizer of $S(\Delta\|\Gamma )$ over all free states $\Gamma$.

The nonfreeness of a many-fermion state $\Delta$ is its entropy relative to the free “reference" state $\Gamma_\Delta$. Other authors have essayed similar relative entropy measures of correlation strength, using various other uncorrelated reference states chosen [*ad hoc*]{} on physical grounds [@Byczuk; @ByczukErrata]. They proposed to use judicious choices of “physically well-known uncorrelated states" $\Gamma$ as reference states, avowedly because [@Byczuk; @footnote] they did not know which choice of $\Gamma$ minimizes $S(\Delta\|\Gamma)$. Shortly afterward, Held and Mauser [@MauserHeld] 