Mathematical Foundations of Nonextensive Statistical Mechanics

✍ Scribed by Sabir Umarov, Tsallis Constantino

• Publisher: World Scientific
• Year: 2022
• Tongue: English
• Leaves: 337
• Category: Library

✦ Synopsis

The book is devoted to the mathematical foundations of nonextensive statistical mechanics. This is the first book containing the systematic presentation of the mathematical theory and concepts related to nonextensive statistical mechanics, a current generalization of Boltzmann-Gibbs statistical mechanics introduced in 1988 by one of the authors and based on a nonadditive entropic functional extending the usual Boltzmann-Gibbs-von Neumann-Shannon entropy. Main mathematical tools like the q-exponential function, q-Gaussian distribution, q-Fourier transform, q-central limit theorems, and other related objects are discussed rigorously with detailed mathematical rational. The book also contains recent results obtained in this direction and challenging open problems. Each chapter is accompanied with additional useful notes including the history of development and related bibliographies for further reading.

✦ Table of Contents

Dedication
Preface
Acknowledgement
Contents
1. Background. q-Generalization of Boltzmann–Gibbs Entropy
2. q-Algebra and q-Generalizations of Some Elementary Functions
3. q-Fourier Transform and Its Properties
4. q-Central Limit Theorems
5. (q, α)-Stable Distributions
6. Applications and Observations of q-GaussianDistributions
7. Some Open Problems
Bibliography
Index