  State-of-the-art simulation tools for non-equilibrium quantum transport
systems typically take the current-carrier occupations to be described in terms
of equilibrium distribution functions characterised by two different
electro-chemical potentials, while for the description of electronic exchange
and correlation, the local density approximation (LDA) to density functional
theory (DFT) is generally used.
  However this involves an inconsistency because the LDA is based on the h
omogeneous electron gas in equilibrium, while the system is not in equilibrium
and may be far from it. In this paper we analyze this inconsistency by studying
the interplay between non-equilibrium occupancies obtained from a maximum
entropy approach and the Hartree-Fock exchange energy, single-particle spectrum
and exchange hole, for the case of a two-dimensional homogeneous electron gas.
The current-dependence of the local exchange potential is also discussed.
  It is found that the single-particle spectrum and exchange hole have a
significant dependence on the current which has not been taken into account in
practical calculations. The exchange energy and the local exchange potential,
however, are shown to change very little with respect to their equilibrium
counterparts.
  The weak dependence of these quantities on the current is explained in terms
of the symmetries of the exchange hole.
