Flexible vs rigid constraints in statistical mechanics

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Abstract
Rigid constraints fix the value of some degrees of freedom, such as bond lengths or angles, in the allowed motion of a system. ’’Flexible constraints’’ is a term which describes the limit as the amplitudes of vibration in these coordinates are made to approach zero by infinitely increasing appropriate force constants. The statistical properties of flexibly and rigidly constrained systems are, in general, different. How the difference arises is illustrated in terms of a simple model. A suggestion of Fixman on how to compensate for the difference in terms of an effective potential is rederived for the statics of the model. This paper examines dynamical problems more deeply. The quantum mechanical case is also discussed.