Kinetic theory of reacting fluid mixtures. I. The BBGKY hierarchy in arrangement channel quantum mechanics

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Abstract
The statistical mechanics of reacting fluid mixtures is considered using arrangement channel quantum mechanics. In this theory, the many body wave function, ψ, is expressed in terms of arrangement channel components ψα which satisfy coupled time dependent equations. Using the properties of the ψα, we obtain the corresponding generalization of the density matrix ρ denoted ραβ and the quantum ’’Liouville equation’’ which it satisfies. Reduced arrangement channel density matrices are introduced and are found to satisfy a generalization of the BBGKY hierarchy for reactive mixtures. The properties of the hierarchy are explored, and it is shown that the streaming terms in succeeding members of the hierarchy have increasing connectivity appropriate to the number of atoms in the contributing arrangement channels. The resulting hierarchy can serve as the rigorous starting point for developing statistical theories of reactive fluids. For example, it can be used to derive a Boltzmann equation appropriate to reacting gaseous mixtures.