Introduction to Nonextensive Statistical Mechanics
Approaching a Complex World
2009, XVIII, 382p. 238 illus., 40 illus. in color.
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Generalization of the ubiquitous Boltzmann-Gibbs theory
First pedagogical book on the subject, written by the proponent of the theory
Many applications to interdisciplinary complex phenomena in virtually all sciences, ranging from physics to medicine, from economics to biology, through signal and image processing and others
Detailed derivation of results
Many detailed illustrations
Brief presentation of Boltzmann-Gibbs statistical mechanics
Detailed presentation of Nonextensive Statistical Mechanics (for the first time)
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.