Nonextensive Statistical Mechanics

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340 Appendix B Escort Distributions and q-Expectation ValuesFig. B.3 Behavior, as functions of the number of deviates, of the variance V [X] ≡ σ 2 and theq-variance V q [X] ≡ σq 2 of typical, stochastically generated, q-Gaussians. Top: For q = 1.4( 5/3); lim # of deviates→∞ V [X] =∞,andlim # of deviates→∞ V 2.75 [X] = 9. Noticehow huge is the ordinate scale (from [627]).
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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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Part IVLast (But Not Least)
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306 8 Final Comments and Perspectiv
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Page 674: Appendix AUseful Mathematical Formu
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Page 686: Appendix BEscort Distributions and
Page 690: B.1 First Example 33721.5< x > (n)<
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Page 700: Bibliography1. J.W. Gibbs, Elementa
Page 704: Bibliography 34541. A. Rapisarda an
Page 708: Bibliography 34784. A.N. Kolmogorov
Page 712: Bibliography 349123. T. Schneider,
Page 716: Bibliography 351178. A. Campa, A. G
Page 720: Bibliography 353230. S. Abe and A.K
Page 724: Bibliography 355279. K. Briggs and
Page 728: Bibliography 357329. T. Kodama, H.-
Page 732: Bibliography 359Italy), eds. C. Bec
Page 736: Bibliography 361431. M.J.A. Bolzan,
Page 740: Bibliography 363479. T. Cattaert, M
Page 744: 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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