Introduction to Nonextensive Statistical Mechanics: Approaching a Complex WorldMetaphors, 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.
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Contents
Historical Background and Physical Motivations | 3 |
Learning with BoltzmannGibbs Statistical Mechanics 19 | 18 |
Nonextensive Statistical Mechanics | 37 |
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 |
and Growth | 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 |