Introduction to nonextensive statistical mechanics: approaching a complex world

Constantino Tsallis (auth.)0387853588, 9780387853581

This book focuses on nonextensive statistical mechanics, a current generalization of Boltzmann-Gibbs (BG) statistical mechanics, one of the greatest monuments of contemporary physics. Conceived more than 130 years ago by Maxwell, Boltzmann and Gibbs, the BG theory exhibits many impressive successes in physics, chemistry, mathematics, and computational sciences. Presently, several thousands of publications by scientists around the world have been dedicated to its nonextensive generalization. A variety of applications have emerged in complex systems and its mathematical grounding is by now well advanced. A pedagogical introduction to its concepts – nonlinear dynamics, extensivity of the nonadditive entropy, global correlations, and extensions of the standard central limit theorems, among others – is presented in this book, as well as a selection of paradigmatic applications in various sciences and diversified experimental verifications of some of its predictions.

Introduction to Nonextensive Statistical Mechanics is suitable for students and researchers with an interest in complex systems and statistical physics.

Table of contents :
Front Matter….Pages I-XVIII
Front Matter….Pages 1-1
Historical Background and Physical Motivations….Pages 3-17
Learning with Boltzmann–Gibbs Statistical Mechanics….Pages 19-36
Generalizing What We Learnt: Nonextensive Statistical Mechanics….Pages 37-106
Front Matter….Pages 107-107
Stochastic Dynamical Foundations of~Nonextensive Statistical Mechanics….Pages 109-150
Deterministic Dynamical Foundations of Nonextensive Statistical Mechanics….Pages 151-207
Generalizing Nonextensive Statistical Mechanics….Pages 209-218
Front Matter….Pages 219-219
Thermodynamical and Nonthermodynamical Applications….Pages 221-301
Front Matter….Pages 302-302
Final Comments and Perspectives….Pages 305-327
Back Matter….Pages 329-382