  We present an ab-initio approach for grand canonical ensembles in thermal
equilibrium with local or nonlocal external potentials based on the one-reduced
density matrix. We show that equilibrium properties of a grand canonical
ensemble are determined uniquely by the eq-1RDM and establish a variational
principle for the grand potential with respect to its one-reduced density
matrix. We further prove the existence of a Kohn-Sham system capable of
reproducing the one-reduced density matrix of an interacting system at finite
temperature. Utilizing this Kohn-Sham system as an unperturbed system, we
deduce a many-body approach to iteratively construct approximations to the
correlation contribution of the grand potential.
