  The density matrix of a non-relativistic quantum system, divided into $N$
sub-systems, is rewritten in terms of the set of all partitioned density
matrices for the system. For the case where the different sub-systems are
distinguishable, we derive a hierarchy of equations of motion linking the
dynamics of all the partitioned density matrices, analogous to the
"Schwinger-Dyson" hierarchy in quantum field theory. The special case of a set
of $N$ coupled spin-$1/2$ "qubits" is worked out in detail. The equations are
then rewritten in terms of a set of "entanglement correlators", which comprise
all the possible correlation functions for the system - this case is worked out
for coupled spin systems. The equations of motion for these correlators can be
written in terms of a first-order differential equation for an entanglement
correlator supervector.
