Next Article in Journal
On a Generalized Entropy Measure Leading to the Pathway Model with a Preliminary Application to Solar Neutrino Data
Next Article in Special Issue
Examples of the Application of Nonparametric Information Geometry to Statistical Physics
Previous Article in Journal
Methods of Evaluating Thermodynamic Properties of Landscape Cover Using Multispectral Reflected Radiation Measurements by the Landsat Satellite
Previous Article in Special Issue
Solutions of Some Nonlinear Diffusion Equations and Generalized Entropy Framework
Article Menu

Export Article

Open AccessReview
Entropy 2013, 15(10), 3983-4010; doi:10.3390/e15103983

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

Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
Received: 29 July 2013 / Revised: 17 September 2013 / Accepted: 17 September 2013 / Published: 25 September 2013
(This article belongs to the collection Advances in Applied Statistical Mechanics)
View Full-Text   |   Download PDF [303 KB, uploaded 24 February 2015]   |  

Abstract

We present the main features of the mathematical theory generated by the κ-deformed exponential function exp k (x) = ( 1 + k 2 x 2 + kx) 1 k , with 0 κ < 1, 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.
Keywords: κ-statistical mechanics; κ-mathematics; κ-exponential; κ-logarithm; power-law tailed statistical distributions κ-statistical mechanics; κ-mathematics; κ-exponential; κ-logarithm; power-law tailed statistical distributions
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Kaniadakis, G. Theoretical Foundations and Mathematical Formalism of the Power-Law Tailed Statistical Distributions. Entropy 2013, 15, 3983-4010.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top