  In this paper, we formally demonstrate that the non-equilibrium density
matrix developed by Hershfield for the steady state has the form of a
McLennan-Zubarev non-equilibrium ensemble. The correction term in this pseudo
equilibrium Gibbs-like ensemble is directly related to the entropy production
in the quantum open system. The fact the both methods state that a
non-equilibrium steady state can be mapped onto a pseudo-equilibrium, permits
us to develop non-equilibrium quantities from formal expressions equivalent to
the equilibrium case. We provide an example: the derivation of a
non-equilibrium distribution function for the electron population in a
scattering region in the context of quantum transport.
