  We study the macroscopic dynamics of fermion and quantum-spin systems with
long-range, or mean-field, interactions, which turns out to be equivalent to an
intricate combination of classical and short-range quantum dynamics. In this
paper we focus on the \emph{quantum} part of the long-range macroscopic
dynamics. The classical part is studied in a companion paper. Altogether, the
results obtained are far beyond previous ones and required the development of a
suitable mathematical framework. The entanglement of classical and quantum
worlds is noteworthy, opening new theoretical perspectives, and is shown here
to be a consequence of the highly non-local character of long-range, or
mean-field, interactions.
