  We develop a new theoretical framework for describing steady-state quantum
transport phenomena, based on the general maximum-entropy principle of
non-equilibrium statistical mechanics. The general form of the many-body
density matrix is derived, which contains the invariant part of the current
operator that guarantees the non-equilibrium and steady-state character of the
ensemble. Several examples of the theory are given, demonstrating the
relationship of the present treatment to the widely-used scattering-states
occupation schemes at the level of the self-consistent single-particle
approximation.
