On the $q-$parameter spectrum of generalized information-entropy measures with no cut-off prescriptions

摘要

After studying some properties of the generalized exponential and logarithmicfunction, in particular investigating the domain where the first maintainsitself real and positive, and outlining how the known dualities $q\leftrightarrow \frac{1}{q}$ and $q \leftrightarrow 2-q$ play an importantrole, we shall examine the set of q-deforming parameters that allow generalizedcanonical maximum entropy probability distributions (MEPDs) to maintain itselfpositive and real without cut-off prescriptions. We determine the set ofq-deforming parameters for which a generalized statistics with discrete butunbound energy states is possible.