  In this article, we present a set of hierarchy Bloch equations for the
reduced density operators in either canonical or grand canonical ensembles in
the occupation number representation. They provide a convenient tool for
studying the equilibrium quantum statistical mechanics for some model systems.
As an example of their applications, we solve the equations for the model
system with a pairing Hamiltonian. With the aid of its symplectic group
symmetry, we obtain the statistical reduced density matrices with different
orders. As a special instance for the solutions, we also get the reduced
density matrices of the ground state for a superconductor.
