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 language | English |
|---|---|
| Article number | 103301 |
| Journal | Journal of Mathematical Physics |
| Volume | 50 |
| Issue number | 10 |
| DOIs | |
| Publication status | Published - 2009 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
Cite this
A note on the definition of deformed exponential and logarithm functions. / Oikonomou, Thomas; Bagci, G. Baris.
In: Journal of Mathematical Physics, Vol. 50, No. 10, 103301, 2009.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A note on the definition of deformed exponential and logarithm functions
AU - Oikonomou, Thomas
AU - Bagci, G. Baris
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=70350725947&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=70350725947&partnerID=8YFLogxK
U2 - 10.1063/1.3227657
DO - 10.1063/1.3227657
M3 - Article
AN - SCOPUS:70350725947
VL - 50
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
SN - 0022-2488
IS - 10
M1 - 103301
ER -