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A finite-temperature perturbation theory for the grand canonical ensemble isintroduced that expands chemical potential in a perturbation series andconserves the average number of electrons, ensuring charge neutrality of thesystem at each perturbation order. Two classes of (sum-over-state and reduced)analytical formulas are obtained in a straightforward, algebraic,time-independent derivation for the first-order corrections to chemicalpotential, grand potential, and internal energy, with the aid of severalidentities of the Boltzmann sums also introduced in this study. These formulasare numerically verified against benchmark data from thermal full configurationinteraction. In the zero-temperature limit, the finite-temperature perturbationtheory reduces analytically to and is consistent with the M{\o}ller-Plessetperturbation theory, but only for a nondegenerate ground state. For adegenerate ground state, its correct zero-temperature limit is not theM{\o}ller-Plesset perturbation theory, but the Hirschfelder-Certain degenerateperturbation theory.

Converging finite-temperature many-body perturbation theory that conserves the average number of electrons