A recent analysis of the normal modes of vibration of a ring formed from an elastic rod was taken as the basis of a theory of the classical (high-temperature limit) statistical thermodynamics of a canonical ensemble of DNA minicricles (miniplasmids), each having a given number N of base pairs and given linking number difference #DELTA#L_k. Here, the vibrational modes are taken to be quantum mechanical in nature, which, in effect, generalizes the treatment to all temperatures. It is found that significant differences between the ensemble average of the writhing number as determined from the general theory and that calculated using the classical formalism do not appear except at very low temperatures.
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