A note on the definition of deformed exponential and logarithm functions

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dc.contributor.authorOikonomou, Thomas
dc.contributor.authorBagci, G. Baris
dc.date.accessioned2019-10-27T20:45:45Z
dc.date.available2019-10-27T20:45:45Z
dc.date.issued2009
dc.departmentEge Üniversitesien_US
dc.description.abstractThe 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 Reacutenyi entropy.en_US
dc.description.sponsorshipTUBITAK (Turkish Agency)Turkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [108T013]; CNPq (Brazilian Agency)National Council for Scientific and Technological Development (CNPq) [505453/2008-8]en_US
dc.description.sponsorshipT.O. acknowledges fruitful remarks from E. M. F. Curado, C. Tsallis, R. S. Wedemann, and L. Lacasa. We thank U. Tirnakli for a careful reading of the manuscript and bringing Ref. 6 to our attention. G. B. B. was supported by TUBITAK (Turkish Agency) under Research Project No. 108T013. T.O. was supported by CNPq (Brazilian Agency) under Research Project No. 505453/2008-8.en_US
dc.identifier.doi10.1063/1.3227657
dc.identifier.issn0022-2488
dc.identifier.issn1089-7658
dc.identifier.issn0022-2488en_US
dc.identifier.issn1089-7658en_US
dc.identifier.issue10en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.urihttps://doi.org/10.1063/1.3227657
dc.identifier.urihttps://hdl.handle.net/11454/42308
dc.identifier.volume50en_US
dc.identifier.wosWOS:000271357600031en_US
dc.identifier.wosqualityQ3en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherAmer Inst Physicsen_US
dc.relation.ispartofJournal of Mathematical Physicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectBoltzmann equationen_US
dc.subjectentropyen_US
dc.subjectfree energyen_US
dc.subjectstatisticsen_US
dc.titleA note on the definition of deformed exponential and logarithm functionsen_US
dc.typeArticleen_US

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