A note on the definition of deformed exponential and logarithm functions
Küçük Resim Yok
Tarih
2009
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Amer Inst Physics
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
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 Reacutenyi entropy.
Açıklama
Anahtar Kelimeler
Boltzmann equation, entropy, free energy, statistics
Kaynak
Journal of Mathematical Physics
WoS Q Değeri
Q3
Scopus Q Değeri
Q2
Cilt
50
Sayı
10
