Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World

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Springer Science & Business Media, Mar 11, 2009 - Science - 382 pages

Metaphors, generalizations and unifications are natural and desirable ingredients of the evolution of scientific theories and concepts. Physics, in particular, obviously walks along these paths since its very beginning. 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 uncountable – some of them impressive – successes in physics, chemistry, mathematics, and computational sciences, to name a few. Presently, more than two thousand publications, by over 1800 scientists around the world, have been dedicated to the nonextensive generalization. Remarkable applications have emerged, and its mathematical grounding is by now relatively well established. A pedagogical introduction to its concepts – nonlinear dynamics, extensivity of the nonadditive entropy, global correlations, generalization of the standard CLT’s, among others – is presented in this book as well as a selection of paradigmatic applications in various sciences together with diversified experimental verifications of some of its predictions.

  • This is the first pedagogical book on the subject, written by the proponent of the theory
  • Presents 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
  • Offers a detailed derivation of results, illustrations and for the first time detailed presentation of Nonextensive Statistical Mechanics
 

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Contents

Historical Background and Physical Motivations
3
Stochastic Dynamical Foundations of Nonextensive Statistical
109
Deterministic Dynamical Foundations of Nonextensive Statistical
151
Generalizing Nonextensive Statistical Mechanics 209
208
Thermodynamical and Nonthermodynamical Applications
221
andGrowth
259
Final Comments and Perspectives
305
Appendix A Useful Mathematical Formulae
329
Appendix B Escort Distributions and qExpectation Values
335
Bibliography
343
Index 381
358
Copyright

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About the author (2009)

http://tsallis.cat.cbpf.br/biblio.htm

Born in Athens-Greece, grew up in Argentina, Docteur d’ Etat from the University of Paris, established in Brazil since 1975, where he acquired the Brazilian citizenship. Many of the most recent theoretical results have, as co-author, Murray Gell-Mann, Nobel Laureate in Physics for his discovery of quarks. The author has recently done a two-year-long visit as researcher at the Santa Fe Institute, New Mexico.

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