Nonextensive Statistical Mechanics

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276 7 Thermodynamical and Nonthermodynamical ApplicationsFig. 7.75 Typical runs of the GSA algorithm. E t vs. t (MCS) for random initial conditions andT (1) = 100. Acceptance parameter q A = 1and(a) q V = 1, (b) q V = 2, (c) q V = 2.5, and(d) q V = 2.7 (from [626]).Fig. 7.76 Mean convergence time vs. q V .Thesolid line is a guide to the eye. The mean convergencetime for q V = 1 is about 50,000. By taking q V ≃ 2.6, there is a gain in computer time of afactor close to 100 (from [626]).
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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 522: 250 7 Thermodynamical and Nonthermo
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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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