Classical Statistical Mechanics of Constraints: A Theorem and Application to Polymers

A classical system of mass points subject to holonomic constraints has a kinetic energy dependent on the coordinates as well as the moments of the remaining degrees of freedom. Coordinate averages formed in the reduced space of unconstrained coordinates and their conjugate momenta then involve a metric determinant that may be difficult to evaluate. A theorem is derived that permits a relatively easy evaluation when the constraints are distances between particles, and an application is made to a Kramers type freely jointed chain.