We calculate the quantum second virial coefficients and their contributions to the canonical entropy for twohyphen; and threehyphen;dimensional systems interacting with a hardhyphen;core squarehyphen;well potential. This provides three examples of quantum mechanical systems in which the canonical entropy becomes greater than the canonical entropy for the corresponding ideal (noninteracting) systems over a finite temperature interval when Boltzmann statistics is assumed, thus contradicting the conjecture of Baierlein. In addition, low temperature expansions of the second virial coefficient and its contributions to the canonical entropy are made for the general threehyphen;dimensional system in powers of the (reduced) temperature.
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