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

TL;DR

This paper explores the properties of generalized exponential and logarithmic functions, focusing on the range of q-parameters that produce valid, positive, and real maximum entropy probability distributions without the need for cut-offs.

Contribution

It identifies the specific q-parameter ranges that allow for positive, real generalized distributions in unbounded energy systems without cut-offs.

Findings

Determines the domain of q for real, positive generalized exponential functions.

Identifies q-values that yield valid maximum entropy distributions without cut-offs.

Analyzes dualities in q-parameters affecting distribution properties.

Abstract

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