Two-site Hubbard model, the Bardeen-Cooper-Schrieffer model, and the concept of correlation entropy

Exactly solvable models (the two-electron two-site Hubbard model and the Bardeen-Cooper-Schrieffer model) are revisited in terms of their natural occupation numbers (eigenvalues of the true, i.e., correlated, one-particle density matrix). Entropylike expressions that may serve as measures of the correlation strength are related to possible reference states for the definition of correlation and discussed as functions of the system parameters.