Nonextensive Statistical Mechanics

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206 5 Deterministic Dynamical Foundations of Nonextensive Statistical Mechanics(a)(b)(a)(b)Fig. 5.63 The q-triplet as measured from the magnetic field strength of the solar wind. The three sets of curves correspond to daily averages of the data sent in1989 (40 AU) and in 2002 (85 AU) by the NASA Voyager 1 spacecraft. See details in [361]. Within the errors bars, these three values have been heuristicallyapproached [199] by the values (qsen, qrel, qstat) = (−0.5, 4, 7/4).
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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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Page 386: 180 5 Deterministic Dynamical Found
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7.1 Physics 2337.1.4 FingeringWhen
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7.1 Physics 235Fig. 7.16 The vertic
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7.1 Physics 237Fig. 7.19 Measured (
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7.1 Physics 239Fig. 7.23 Time evolu
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7.1 Physics 2417.1.8 Astrophysics7.
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7.1 Physics 243Fig. 7.28 Top: Fits
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7.1 Physics 245Fig. 7.30 Log-Log pl
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7.1 Physics 247Fig. 7.32 Dependence
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7.1 Physics 249Fig. 7.36 Data colla
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7.1 Physics 251Fig. 7.39 Cumulative
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7.1 Physics 253a0-1--2-3-4-5- - - -
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7.1 Physics 2551.25fit in Fig.2Eq.(
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7.1 Physics 2574.0q relc3.53.02.52.
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7.2 Chemistry 259Fig. 7.49 (a) Dime
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7.2 Chemistry 261Fig. 7.52 d = 2(a)
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7.2 Chemistry 263Fig. 7.55 Snapshot
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7.2 Chemistry 265Fig. 7.58 Log-log
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7.3 Economics 267Fig. 7.60 Ground-s
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7.4 Computer Sciences 269Fig. 7.64
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7.5 Biosciences 281Fig. 7.82 Image
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7.8 Scale-Free Networks 283Fig. 7.8
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7.8 Scale-Free Networks 285a1b1cumu
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7.10 Other Sciences 295Fig. 7.102 S
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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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