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Quantum statistical mechanics is formulated as an integral over classicalphase space. Some details of the commutation function for averages arediscussed, as is the factorization of the symmetrization function used for thegrand potential and for the multi-particle density. Three binary choices (eightroutes) for the average energy are shown to be mutually consistent. Anexpression for the phase space function that gives the average virial pressureis derived.

Quantum Statistical Mechanics in Classical Phase Space. Expressions for the Multi-Particle Density, the Average Energy, and the Virial Pressure