Many-body partition function and thermal Hartree-Fock approximations

The hierarchy equations for the quantum thermal density matrices of an asse mbly of interacting particles in an external potential are derived in a com pact form. This approach can complement and finally replace the phenomenolo gical treatment of the thermodynamic properties of quantum gasses. liquids, and solids. We also derive a temperature Hartree-Fock approximation for fe rmions based on the symmetry properties of the exact hierarchy and finally we discuss the present approximation in relation to that of Kaplan and Argy res [T. A. Kaplan and P. N. Argyres, Ann. Phys. (N.Y.) 92, 1 (1975)].