  A finite-temperature many-body perturbation theory is presented that expands
in power series the electronic grand potential, chemical potential, internal
energy, and entropy on an equal footing. Sum-over-states and sum-over-orbitals
analytical formulas for the second-order perturbation corrections to these
thermodynamic properties are obtained in a time-independent, nondiagrammatic,
algebraic derivation, relying on the sum rules of the Hirschfelder-Certain
degenerate perturbation energies in a degenerate subspace as well as nine
algebraic identities for zeroth-order thermal averages of one- through
four-indexed quantities and of products thereof. They reproduce numerically
exactly the benchmark data obtained as the numerical derivatives of the
thermal-full-configuration-interaction results for a wide range of temperature.
