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A classical upper bound for quantum entropy is identified and illustrated, 0\≤ Sq \≤ ln (e \σ² / 2\), involving the variance \σ² in phase space of the classical limit distribution of a given system. A fortiori, this further bounds the corresponding information-theoretical generalizations of the quantum entropy proposed by Renyi.
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Cosmas Zachos (2007) studied this question.
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