  We suggest a generalisation of the expression of the nonequilibrium density
matrix obtained by Hershfield's method for the cases where both heat and charge
steady state currents are present in a quantum open system. The finite-size
quantum system, connected to two temperature and particle reservoirs, is driven
out of equilibrium by the presence of both a temperature gradient and a
chemical potential gradient between the two reservoirs. We show that the NE
density matrix is given by a generalised Gibbs-like ensemble, and is in full
agreement with the general results of the McLennan-Zubarev nonequilibrium
ensembles. The extra non-equilibrium terms are related to the entropy
production in the system and characterise the fluxes of heat and particle.An
explicit example, for the lowest order expansion, is provide for a model system
of non-interacting fermions.
