  It is important that any dynamics method approaches the correct population
distribution at long times. In this paper, we derive a one-body reduced density
matrix dynamics for electrons in energetic contact with a bath. We obtain a
remarkable equation of motion which shows that in order to reach equilibrium
properly, rates of electron transitions depend on the density matrix. Even
though the bath drives the electrons towards a Boltzmann distribution, hole
blocking factors in our equation of motion cause the electronic populations to
relax to a Fermi-Dirac distribution. These factors are an old concept, but we
show how they can be derived with a combination of time-dependent perturbation
theory, and the extended normal ordering of Mukherjee and Kutzelnigg. The
resulting non-equilibrium kinetic equations generalize the usual Redfield
theory to many-electron systems, while ensuring that the orbital occupations
remain between zero and one. In numerical applications of our equations, we
show that relaxation rates of molecules are not constant because of the
blocking effect. Other applications to model atomic chains are also presented
which highlight the importance of treating both dephasing and relaxation.
Finally we show how the bath localizes the electron density matrix.
