A note on the definition of deformed exponential and logarithm functions

Journal of Mathematical Physics - Tập 50 Số 10 - 2009
Thomas Oikonomou1,2, G. Baris Bagci3
1Centro Brasileiro de Pesquisas Fisicas, Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil and Institute of Physical Chemistry, National Center for Scientific Research "Demokritos," 15310 Athens, Greece
2National Center for Scientific Research “Demokritos 1 , Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil and Institute of Physical Chemistry, ,” 15310 Athens, Greece
3Ege University 2 Department of Physics, Faculty of Science, , 35100 Izmir, Turkey

Tóm tắt

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 Rényi entropy.

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Journal of Mathematical Physics

Tập 50 Số 10

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