  We construct a class of quantum stochastic models of reservoir driven
many-particle systems that are the natural counterparts of certain extensively
studied classical ones, which have been shown to exhibit good hydrodynamical
behaviour. Our treatment of these models achieves two main aims. The first is
to show that they enjoy the hydrodynamical properties of their classical
counterparts. The second is to show that they satisfy the key assumptions of
the general quantum macrostatistical scheme, presented in earlier works by the
author, which served to expose certain generic large scale features of
nonequilibrium steady states, e.g. the long range of the hydrodynamical
correlations that they carry. In this way we establish the viability of that
scheme.
