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

Constructing non-equilibrium statistical ensemble formalism based on Subdynamics