Nonextensive Statistical Mechanics

More documents

Recommendations

Info

134 4 Stochastic Dynamical Foundations of Nonextensive Statistical MechanicsFig. 4.15 Successive discretizations (with typical values of N) ofaq = 3/4 q-Gaussian (from[244]).Fig. 4.16 Q N,n − 1 as a function of n for N = 500 and different values of q =−1, −1/2, 0, 1/4, 1/2 for discretizations D1 (top) andD2(bottom). Strict scale invariance is observedfor q = 0 and discretization D1 (from [244]).
Page 2:
Introduction to Nonextensive Statis
Page 6:
Constantino TsallisCentro Brasileir
Page 10:
PrefaceIn 1902, after three decades
Page 14:
Prefaceixequation inspired by the p
Page 18:
Prefacexinearby. 4 Nonextensive sta
Page 22:
Prefacexiiicircular epicycles. So w
Page 26:
ContentsPart IBasics or How the The
Page 30:
Contentsxvii5.2 Low-Dimensional Con
Page 34:
Part IBasics or How the Theory Work
Page 38:
4 1 Historical Background and Physi
Page 42:
Page 46:
Page 50:
10 1 Historical Background and Phys
Page 54:
Page 58:
Page 62:
Page 66:
Chapter 2Learning with Boltzmann-Gi
Page 70:
2.1 Boltzmann-Gibbs Entropy 212.1.2
Page 74:
2.1 Boltzmann-Gibbs Entropy 232.1.2
Page 78:
2.1 Boltzmann-Gibbs Entropy 25where
Page 82:
2.1 Boltzmann-Gibbs Entropy 27the s
Page 86:
2.2 Kullback-Leibler Relative Entro
Page 90:
2.3 Constraints and Entropy Optimiz
Page 94:
2.4 Boltzmann-Gibbs Statistical Mec
Page 98:
2.4 Boltzmann-Gibbs Statistical Mec
Page 102:
Chapter 3Generalizing What We Learn
Page 106:
3.1 Playing with Differential Equat
Page 110:
3.2 Nonadditive Entropy S q 41We sh
Page 114:
3.2 Nonadditive Entropy S q 43This
Page 118:
3.2 Nonadditive Entropy S q 453.2.2
Page 122:
3.2 Nonadditive Entropy S q 47we ca
Page 126:
3.2 Nonadditive Entropy S q 49S BG
Page 130:
3.2 Nonadditive Entropy S q 51with
Page 134:
3.2 Nonadditive Entropy S q 53whose
Page 138:
3.3 Correlations, Occupancy of Phas
Page 142:
Page 146:
Page 150:
Page 154:
Page 158:
Page 162:
Page 166:
Page 170:
Page 174:
Page 178:
Page 182:
Page 186:
Page 190:
Page 194:
Page 198:
3.4 q-Generalization of the Kullbac
Page 202:
3.4 q-Generalization of the Kullbac
Page 206:
3.5 Constraints and Entropy Optimiz
Page 210:
3.6 Nonextensive Statistical Mechan
Page 214:
Page 218:
Page 222:
Page 226:
3.7 About the Escort Distribution a
Page 230:
3.7 About the Escort Distribution a
Page 234:
3.8 About Universal Constants in Ph
Page 238:
3.9 Various Other Entropic Forms 10
Page 242: Part IIFoundations or Why the Theor
Page 246: 110 4 Stochastic Dynamical Foundati
Page 296: 4.7 Central Limit Theorems 135Fig.
Page 300: 4.7 Central Limit Theorems 137See F
Page 316: 4.8 Generalizing the Langevin Equat
Page 320: 4.8 Generalizing the Langevin Equat
Page 324: 4.9 Time-Dependent Ginzburg-Landau
Page 328: Chapter 5Deterministic Dynamical Fo
Page 332: 5.1 Low-Dimensional Dissipative Map
Page 344:
5.1 Low-Dimensional Dissipative Map
Page 348:
Page 352:
Page 356:
5.2 Low-Dimensional Conservative Ma
Page 360:
Page 364:
Page 368:
Page 372:
Page 376:
Page 380:
Page 384:
5.3 High-Dimensional Conservative M
Page 388:
5.3 High-Dimensional Conservative M
Page 392:
5.4 Many-Body Long-Range-Interactin
Page 396:
Page 400:
Page 404:
Page 408:
5.5 The q-Triplet 1910.500.48N = 20
Page 412:
5.5 The q-Triplet 19310 010 -1N = 2
Page 416:
5.6 Connection with Critical Phenom
Page 420:
5.7 A Conjecture on the Time and Si
Page 424:
Page 428:
Page 432:
Page 436:
Page 440:
p5.7 A Conjecture on the Time and S
Page 444:
210 6 Generalizing Nonextensive Sta
Page 448:
Page 452:
Page 456:
Page 460:
Page 464:
Chapter 7Thermodynamical and Nonthe
Page 468:
7.1 Physics 223Fig. 7.1 Computation
Page 472:
7.1 Physics 225hypergeometric funct
Page 476:
7.1 Physics 227Fig. 7.6 The dashed
Page 480:
7.1 Physics 229Fig. 7.7 Example sha
Page 484:
7.1 Physics 231Fig. 7.11 Experiment
Page 488:
7.1 Physics 2337.1.4 FingeringWhen
Page 492:
7.1 Physics 235Fig. 7.16 The vertic
Page 496:
7.1 Physics 237Fig. 7.19 Measured (
Page 500:
7.1 Physics 239Fig. 7.23 Time evolu
Page 504:
7.1 Physics 2417.1.8 Astrophysics7.
Page 508:
7.1 Physics 243Fig. 7.28 Top: Fits
Page 512:
7.1 Physics 245Fig. 7.30 Log-Log pl
Page 516:
7.1 Physics 247Fig. 7.32 Dependence
Page 520:
7.1 Physics 249Fig. 7.36 Data colla
Page 524:
7.1 Physics 251Fig. 7.39 Cumulative
Page 528:
7.1 Physics 253a0-1--2-3-4-5- - - -
Page 532:
7.1 Physics 2551.25fit in Fig.2Eq.(
Page 536:
7.1 Physics 2574.0q relc3.53.02.52.
Page 540:
7.2 Chemistry 259Fig. 7.49 (a) Dime
Page 544:
7.2 Chemistry 261Fig. 7.52 d = 2(a)
Page 548:
7.2 Chemistry 263Fig. 7.55 Snapshot
Page 552:
7.2 Chemistry 265Fig. 7.58 Log-log
Page 556:
7.3 Economics 267Fig. 7.60 Ground-s
Page 560:
7.4 Computer Sciences 269Fig. 7.64
Page 564:
Page 568:
Page 572:
Page 576:
Page 580:
Page 584:
7.5 Biosciences 281Fig. 7.82 Image
Page 588:
7.8 Scale-Free Networks 283Fig. 7.8
Page 592:
7.8 Scale-Free Networks 285a1b1cumu
Page 596:
Page 600:
Page 604:
Page 608:
Page 612:
7.10 Other Sciences 295Fig. 7.102 S
Page 616:
7.10 Other Sciences 297Fig. 7.105 F
Page 620:
7.10 Other Sciences 299Fig. 7.109 Z
Page 624:
7.10 Other Sciences 301Fig. 7.112 C
Page 628:
Chapter 8Final Comments and Perspec
Page 632:
8.1 Falsifiable Predictions and Con
Page 636:
8.2 Frequently Asked Questions 309i
Page 640:
8.2 Frequently Asked Questions 311B
Page 644:
8.2 Frequently Asked Questions 313(
Page 648:
8.2 Frequently Asked Questions 315o
Page 652:
8.2 Frequently Asked Questions 317p
Page 656:
8.2 Frequently Asked Questions 319n
Page 660:
8.2 Frequently Asked Questions 321L
Page 664:
8.2 Frequently Asked Questions 323(
Page 668:
8.2 Frequently Asked Questions 3254
Page 672:
8.3 Open Questions 327This is a fre
Page 676:
330 Appendix A Useful Mathematical
Page 680:
Page 684:
Page 688:
336 Appendix B Escort Distributions
Page 692:
Page 696:
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,
Page 748:
Bibliography 367579. G.A. Tsekouras
Page 752:
Bibliography 369631. J. Schulte, No
Page 756:
Bibliography 371678. D. Fuks, S. Do
Page 760:
Bibliography 373723. L.J. Yang, M.P
Page 764:
Bibliography 375767. S. Sun, L. Zha
Page 768:
Bibliography 377813. S. Abe, Tsalli
Page 772:
Bibliography 379862. S. Boccaletti,
Page 776:
382 IndexKekule, ixKepler, xiiKrylo
show all

Nonextensive Statistical Mechanics

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?