  The ground-state properties of the Hubbard model with attractive local
pairing interactions are investigated in the framework of lattice
density-functional theory. A remarkable correlation is revealed between the
interaction-energy functional $W[\boldsymbol{\eta}]$ corresponding to the
Bloch-state occupation-number distribution $\eta_{\boldsymbol{k}\sigma}$ and
the entropy $S[\boldsymbol{\eta}]$ of a system of non-interacting fermions
having the same $\eta_{\boldsymbol{k}\sigma}$. The relation between
$W[\boldsymbol{\eta}]$ and $S[\boldsymbol{\eta}]$ is shown to be approximately
linear for a wide range of ground-state representable occupation-number
distributions $\eta_{\boldsymbol{k}\sigma}$. Taking advantage of this
statistical analogy, a simple explicit ansatz for $W[\boldsymbol{\eta}]$ of the
attractive Hubbard model is proposed, which can be applied to arbitrary
periodic systems. The accuracy of this approximation is demonstrated by
calculating the main ground state properties of the model on several 1D and 2D
bipartite and non-bipartite lattices and by comparing the results with exact
diagonalizations.
