Nonextensive Statistical Mechanics

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272 7 Thermodynamical and Nonthermodynamical ApplicationsCumulative distributionCumulative distribution1000010004000100 300020001000101000100USA (2000)linear scale00 100 200PI/PI 0Knee(a)110 0 10 1 10 2 10 3 10 4 10 5 10 6PI/PI 010Germany (1998)AnkleKnee(c)110 0 10 1 10 2 10 3GDP/GDP 0Cumulative distributionCumulative distribution100001000100101000100500040003000Brazil (1996)linear scale2000100000 100GDP / GDP 0200Knee(b)110 0 10 1 10 2 10 3 10 4 10 5 10 6GDP/GDP 010UK (1998)Knee(d)110 0 10 1 10 2 10 3GDP/GDP 0Fig. 7.69 Cumulative distribution of the scaled total personal income of the USA counties(a), and the scaled gross domestic product of the Brazilian (b), German (c), and United Kingdom(d) counties. See [596] for further details.q3.83.63.43.23.0USABrazilUK2.8Germany2.61970 1980 1990 2000YearFig. 7.70 Time evolution of the index q for USA (squares), Brazil (circles), United Kingdom (uptriangles), and Germany (down triangles). This means that the economic inequalities are largerin USA, then in Brazil, then United Kingdom, and finally Germany. We also see that inequalitiesare increasing in USA and Brazil, whereas they remain at the same level in United Kingdom andGermany. See [596] for further details.
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Introduction to Nonextensive Statis
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Constantino TsallisCentro Brasileir
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PrefaceIn 1902, after three decades
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Prefaceixequation inspired by the p
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Prefacexinearby. 4 Nonextensive sta
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Prefacexiiicircular epicycles. So w
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ContentsPart IBasics or How the The
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Contentsxvii5.2 Low-Dimensional Con
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Part IBasics or How the Theory Work
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4 1 Historical Background and Physi
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10 1 Historical Background and Phys
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Chapter 2Learning with Boltzmann-Gi
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2.1 Boltzmann-Gibbs Entropy 212.1.2
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2.1 Boltzmann-Gibbs Entropy 232.1.2
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2.1 Boltzmann-Gibbs Entropy 25where
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2.1 Boltzmann-Gibbs Entropy 27the s
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2.2 Kullback-Leibler Relative Entro
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2.3 Constraints and Entropy Optimiz
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2.4 Boltzmann-Gibbs Statistical Mec
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2.4 Boltzmann-Gibbs Statistical Mec
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Chapter 3Generalizing What We Learn
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3.1 Playing with Differential Equat
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3.2 Nonadditive Entropy S q 41We sh
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3.2 Nonadditive Entropy S q 43This
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3.2 Nonadditive Entropy S q 453.2.2
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3.2 Nonadditive Entropy S q 47we ca
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3.2 Nonadditive Entropy S q 49S BG
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3.2 Nonadditive Entropy S q 51with
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3.2 Nonadditive Entropy S q 53whose
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3.3 Correlations, Occupancy of Phas
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3.4 q-Generalization of the Kullbac
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3.4 q-Generalization of the Kullbac
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3.5 Constraints and Entropy Optimiz
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3.6 Nonextensive Statistical Mechan
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3.7 About the Escort Distribution a
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3.7 About the Escort Distribution a
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3.8 About Universal Constants in Ph
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3.9 Various Other Entropic Forms 10
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Part IIFoundations or Why the Theor
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110 4 Stochastic Dynamical Foundati
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152 5 Deterministic Dynamical Found
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10 -5 1 10 100 100010 -5 1 10 100 1
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Chapter 6Generalizing Nonextensive
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6.2 Further Generalizing 211dydx =
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6.2 Further Generalizing 213∫ W{
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6.2 Further Generalizing 215Then, f
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6.2 Further Generalizing 217If f (
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Part IIIApplications or What for th
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222 7 Thermodynamical and Nonthermo
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Page 514: 246 7 Thermodynamical and Nonthermo
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7.10 Other Sciences 297Fig. 7.105 F
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7.10 Other Sciences 299Fig. 7.109 Z
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7.10 Other Sciences 301Fig. 7.112 C
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Chapter 8Final Comments and Perspec
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8.1 Falsifiable Predictions and Con
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8.2 Frequently Asked Questions 309i
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8.2 Frequently Asked Questions 311B
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8.2 Frequently Asked Questions 313(
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8.2 Frequently Asked Questions 315o
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8.2 Frequently Asked Questions 317p
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8.2 Frequently Asked Questions 319n
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8.2 Frequently Asked Questions 321L
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8.2 Frequently Asked Questions 323(
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8.2 Frequently Asked Questions 3254
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8.3 Open Questions 327This is a fre
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330 Appendix A Useful Mathematical
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336 Appendix B Escort Distributions
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Bibliography1. J.W. Gibbs, Elementa
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Bibliography 34541. A. Rapisarda an
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Bibliography 34784. A.N. Kolmogorov
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Bibliography 349123. T. Schneider,
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Bibliography 351178. A. Campa, A. G
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Bibliography 353230. S. Abe and A.K
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Bibliography 355279. K. Briggs and
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Bibliography 357329. T. Kodama, H.-
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Bibliography 359Italy), eds. C. Bec
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Bibliography 361431. M.J.A. Bolzan,
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Bibliography 363479. T. Cattaert, M
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Bibliography 365528. P.H. Chavanis,
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Bibliography 367579. G.A. Tsekouras
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Bibliography 369631. J. Schulte, No
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Bibliography 371678. D. Fuks, S. Do
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Bibliography 373723. L.J. Yang, M.P
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Bibliography 375767. S. Sun, L. Zha
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Bibliography 377813. S. Abe, Tsalli
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Bibliography 379862. S. Boccaletti,
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382 IndexKekule, ixKepler, xiiKrylo
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Nonextensive Statistical Mechanics

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