  Ensemble density functional theory (EDFT) is a promising alternative to
time-dependent density functional theory for computing electronic excitation
energies. Using coordinate scaling, we prove several fundamental exact
conditions in EDFT and illustrate them on the exact singlet bi-ensemble of the
Hubbard dimer. Several approximations violate these conditions, and some
ground-state conditions from quantum chemistry do not generalize to EDFT. The
strong-correlation limit is derived for the dimer, revealing weight-dependent
derivative discontinuities in EDFT.
