  We construct and explore a family of states for quantum systems in contact
with two or more heath reservoirs. The reservoirs are described by equilibrium
distributions. The interaction of each reservoir with the bulk of the system is
encoded in a probability, which characterises the particle exchange among them
and depends in general on the particle momentum. The convex combination of the
reservoir distributions, weighted with the aforementioned probabilities,
defines a new distribution. We establish the existence of an
emission-absorption regime in which the new distribution generates a
non-equilibrium quantum state. We develop a systematic field theory framework
for constructing this state and illustrate its physical properties on a simple
model. In this context we derive the particle current full counting statistics,
the heat current and the Lorenz number. The entropy production and the relative
quantum fluctuations are also determined.
