A note on the definition of deformed exponential and logarithm functions

Thomas Oikonomou, G. Baris Bagci

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17 Citations (Scopus)

Abstract

The recent generalizations of the Boltzmann-Gibbs statistics mathematically rely on the deformed logarithmic and exponential functions defined through some deformation parameters. In the present work, we investigate whether a deformed logarithmic/exponential map is a bijection from R+ /R (set of positive real numbers/all real numbers) to R/ R+, as their undeformed counterparts. We show that their inverse map exists only in some subsets of the aforementioned (co)domains. Furthermore, we present conditions which a generalized deformed function has to satisfy, so that the most important properties of the ordinary functions are preserved. The fulfillment of these conditions permits us to determine the validity interval of the deformation parameters. We finally apply our analysis to Tsallis q -deformed functions and discuss the interval of concavity of the Ŕnyi entropy.

Original languageEnglish
Article number103301
JournalJournal of Mathematical Physics
Volume50
Issue number10
DOIs
Publication statusPublished - Nov 10 2009

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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