Abstract
Since Gibbs synthesized a general equilibrium statistical ensemble theory, many theorists have attempted to generalized the theory to non-equilibrium domain, however the status of the theory of non-equilibrium phenomena can not be said so well established as the Gibbsian ensemble theory. In this work, we present a formalism for the non-equilibrium statistical ensemble based on a subdynamic kinetic equation (SKE) rooted from the Brussels-Austin school and followed by some up-to-date works. The constructed key is to use a similarity transformation between Gibbsian ensembles formalism based on Liouville equation and the subdynamic ensemble formalism based on the SKE. Using this formalism, we study the spin-Boson system, as cases of weak coupling or strongly coupling, and obtain the reduced density operators for the Canonical ensembles easily.
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