  We analyze a class of mean-field (MF) lattice-fermion Hamiltonians and
construct the corresponding grand-canonical density operator for such system.
New terms are introduced, which may be interpreted as local fugacities,
molecular fields, etc. The presence of such terms is an unavoidable consequence
of a consistent statistical description. Although in some cases (e.g. in the
Hartree or the Hartree-Fock-type approximation) the presented formalism is
redundant, in general (e.g. for a renormalized t-J model) it leads to
nontrivial modifications of the thermodynamic properties.
