Nonextensive Statistical Mechanics

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142 4 Stochastic Dynamical Foundations of Nonextensive Statistical MechanicsWe can now present the structure of the q-generalization of the CLTs: seeFig. 4.21. To better understand the structure of the four theorems therein, we shallillustrate some crucial aspects of them.Let us start with the q = 1 cases, i.e., the standard and the Lévy–Gnedenko CLTs.The α = 2 attractor is a Gaussian. The asymptotic behavior of the α
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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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Page 312: 4.7 Central Limit Theorems 143Fig.
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Page 328: Chapter 5Deterministic Dynamical Fo
Page 332: 5.1 Low-Dimensional Dissipative Map
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5.2 Low-Dimensional Conservative Ma
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5.3 High-Dimensional Conservative M
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5.3 High-Dimensional Conservative M
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5.4 Many-Body Long-Range-Interactin
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5.5 The q-Triplet 1910.500.48N = 20
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5.5 The q-Triplet 19310 010 -1N = 2
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5.6 Connection with Critical Phenom
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5.7 A Conjecture on the Time and Si
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p5.7 A Conjecture on the Time and S
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210 6 Generalizing Nonextensive Sta
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Chapter 7Thermodynamical and Nonthe
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7.1 Physics 223Fig. 7.1 Computation
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7.1 Physics 225hypergeometric funct
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7.1 Physics 227Fig. 7.6 The dashed
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7.1 Physics 229Fig. 7.7 Example sha
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7.1 Physics 231Fig. 7.11 Experiment
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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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