2009/07/23 by Thomas Oikonomou, Oikonomou, Thomas, G. Baris Bagci +1
Decision Sciences · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical and Theoretical Analysis #Probabilistic and Robust Engineering Design #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.0907.4067
12 pages, 4 figures
arxiv created 2009/07/23 · openalex publication_date 2009/07/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The recent generalizations of Boltzmann-Gibbs statistics mathematically relies 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, Kaniadakis, Abe and Borges-Roditi deformed functions.