Mathematical Foundations Of Nonextensive Statistical Mechanics

The book is dedicated to the mathematical foundations of nonextensive statistical mechanics, presenting a systematic presentation of the theory and concepts. It discusses main mathematical tools, recent results, and open problems, with additional notes and bibliographies for further reading.

Format: Hardback
Length: 336 pages
Publication date: 03 April 2022
Publisher: World Scientific Publishing Co Pte Ltd

The book delves into the mathematical underpinnings of nonextensive statistical mechanics, presenting a comprehensive and systematic exploration of the theoretical framework and concepts associated with this modern generalization of Boltzmann-Gibbs statistical mechanics. Authored by one of the pioneers in this field, introduced in 1988, nonextensive statistical mechanics builds upon the traditional Boltzmann-Gibbs-von Neumann-Shannon entropy by incorporating a nonadditive entropic functional. This innovative approach offers a deeper understanding of complex systems and their behavior.

To facilitate a rigorous understanding, the book employs a range of mathematical tools, including the q-exponential function, q-Gaussian distribution, q-Fourier transform, q-central limit theorems, and other related objects. Each of these tools is discussed in detail, with comprehensive mathematical rationales provided to elucidate their applications. Furthermore, the book encompasses recent advancements and challenging open problems in the field, providing readers with a glimpse into the current state of research.

To enhance the learning experience, each chapter is accompanied by additional useful notes, encompassing the historical development of the topic and relevant bibliographies for further reading. This comprehensive resource aims to serve as a valuable guide for scholars and researchers seeking to delve into the intricate world of nonextensive statistical mechanics.

ISBN-13: 9789811245152