Theoretical Foundations and Mathematical Formalism of the Power-Law Tailed Statistical Distributions

Entropy

关键词: κ-statistical mechanics;    κ-mathematics;    κ-exponential;    κ-logarithm;    power-law tailed statistical distributions;   

DOI  :  10.3390/e15103983

来源: mdpi

【 摘 要 】

We present the main features of the mathematical theory generated by the κ-deformed exponential function , developed in the last twelve years, which turns out to be a continuous one parameter deformation of the ordinary mathematics generated by the Euler exponential function. The κ-mathematics has its roots in special relativity and furnishes the theoretical foundations of the κ-statistical mechanics predicting power law tailed statistical distributions, which have been observed experimentally in many physical, natural and artificial systems. After introducing the κ-algebra, we present the associated κ-differential and κ-integral calculus. Then, we obtain the corresponding κ-exponential and κ-logarithm functions and give the κ-version of the main functions of the ordinary mathematics.

【 授权许可】

CC BY   
© 2013 by the authors; licensee MDPI, Basel, Switzerland.