  We propose an approach to the realization of many-body quantum state
distributions inspired by combined principles of thermodynamics and mesoscopic
physics. Its essence is a maximum entropy principle conditioned by conservation
laws. We go beyond traditional thermodynamics and condition on the full
distribution of the conserved quantities. The result are quantum state
distributions whose deviations from `thermal states' get more pronounced in the
limit of wide input distributions. We describe their properties in terms of
entanglement measures and discuss strategies for state engineering by methods
of current date experimentation.
