  In this work, we present a general non-equilibrium ensemble formalism based
on the subdynamic equation (SKE). The constructing procedure is to use a
similarity transformation between Gibbsian ensemble formalism and the
non-equilibrium ensemble formalism. The obtained density distribution is a
projected one that can represent essence part of (irreversible) evolution of
the density distribution, by which a generalized reduced density distribution
for the quantum canonical ensembles is studied and applications in Cayley tree
and spin network are discussed.
