  We derive an equation for the time evolution of the natural occupation
numbers for fermionic systems with more than two electrons. The evolution of
such numbers is connected with the symmetry-adapted generalized Pauli exclusion
principle, as well as with the evolution of the natural orbitals and a set of
many-body relative phases. We then relate the evolution of these phases to a
geometrical and a dynamical term, attached to each one of the Slater
determinants appearing in the configuration-interaction expansion of the wave
function.
