Continuity in symmetry and in distinguishability of states: The symmetry numbers of nonrigid molecules

We establish a connection between the concept of distinguishability of quantum states and the concept of continuity in geometric symmetry. For this purpose, we employ the continuous symmetry measure and the nuclear wave functions of a molecule, and evaluate the physical effects of deviation from geometric symmetry. We apply this tool in presenting a unified approach to assigning symmetry numbers to rigid and nonrigid molecules, and readdress, as a specific example, the evaluation of the temperature dependence of the entropy of cyclobutane and cyclohexane. We believe we show that the concept of continuity in geometric symmetry provides a more natural and practical approach to the inherent link between symmetry and entropy, compared with the classical approach.