Quantum statistical mechanics with flexibly constrained degrees of freedom

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Abstract
The statistical mechanical configurational probability distributions are analyzed for two models in which the imposition of constraints in some degrees of freedom affects the reduced distribution function of other nonconstrained degrees of freedom. The classical, semiclassical, and extreme quantum regimes are exhibited for the models when the constraints are imposed by adding harmonic potential energy terms for the constrained variables to the Hamiltonian. In general, the limit obtained for large force constants in the added energies does not correspond to the distribution of the rigidly constrained system. This is in accord with discussions given by Helfand and by Rallison; the present results illustrate their conclusions.