Nonextensive Statistical Mechanics

More documents

Recommendations

Info

xviiiContents7.2.4 Ground State Energy of the Chemical Elements(Mendeleev’s Table) and of Doped Fullerenes . . . . . ...... 2657.3 Economics . . ...............................................2667.4 Computer Sciences . . . . . . ....................................2697.4.1 OptimizationAlgorithms .............................2697.4.2 Analysis of Time Series and Signals . . ..................2757.4.3 Analysis of Images . . . . . .............................2797.4.4 PING Internet Experiment . . . .........................2807.5 Biosciences . ...............................................2817.6 CellularAutomata ..........................................2827.7 Self-Organized Criticality ....................................2837.8 Scale-Free Networks . . . . ....................................2837.8.1 The Natal Model ....................................2907.8.2 Albert–Barabasi Model . . .............................2917.8.3 Non-Growing Model .................................2947.8.4 Lennard–Jones Cluster . . .............................2957.9 Linguistics . . ...............................................2957.10 Other Sciences . . ...........................................295Part IVLast (But Not Least)8 Final Comments and Perspectives.................................3058.1 Falsifiable Predictions and Conjectures, and Their Verifications . . . . 3058.2 Frequently Asked Questions . . . . . .............................3088.3 OpenQuestions ............................................326Appendix A Useful Mathematical Formulae .........................329Appendix B Escort Distributions and q-Expectation Values ............335B.1 FirstExample ..............................................335B.2 Second Example . ...........................................339B.3 Remarks ..................................................339Bibliography .......................................................343Index .............................................................381
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 36: Chapter 1Historical Background and
Page 40: 1.1 Introduction 5whereand∑W A∑
Page 44: 1.2 Background and Indications in t
Page 56: 1.4 A Few Words on the Foundations
Page 68: 20 2 Learning with Boltzmann-Gibbs
Page 84:
28 2 Learning with Boltzmann-Gibbs
Page 88:
Page 92:
Page 96:
Page 100:
Page 104:
38 3 Generalizing What We Learntwho
Page 108:
40 3 Generalizing What We Learnt1e
Page 112:
42 3 Generalizing What We Learnt3q
Page 116:
44 3 Generalizing What We Learntas
Page 120:
46 3 Generalizing What We LearntFig
Page 124:
Page 128:
50 3 Generalizing What We LearntLet
Page 132:
52 3 Generalizing What We Learnt(i)
Page 136:
54 3 Generalizing What We Learntin
Page 140:
56 3 Generalizing What We Learntran
Page 144:
58 3 Generalizing What We Learntg(T
Page 148:
60 3 Generalizing What We LearntThe
Page 152:
62 3 Generalizing What We Learnt1/(
Page 156:
Page 160:
66 3 Generalizing What We LearntLet
Page 164:
68 3 Generalizing What We LearntThe
Page 168:
70 3 Generalizing What We LearntTab
Page 172:
72 3 Generalizing What We LearntTab
Page 176:
74 3 Generalizing What We Learnt100
Page 180:
76 3 Generalizing What We Learntpro
Page 184:
78 3 Generalizing What We Learnt100
Page 188:
80 3 Generalizing What We Learnt0.0
Page 192:
82 3 Generalizing What We Learntspi
Page 196:
84 3 Generalizing What We Learnt0.8
Page 200:
86 3 Generalizing What We LearntThi
Page 204:
88 3 Generalizing What We Learnt1 (
Page 208:
90 3 Generalizing What We Learntwhe
Page 212:
92 3 Generalizing What We LearntIf
Page 216:
94 3 Generalizing What We LearntBec
Page 220:
96 3 Generalizing What We Learntwhe
Page 224:
98 3 Generalizing What We Learntste
Page 228:
100 3 Generalizing What We Learntq-
Page 232:
102 3 Generalizing What We Learntwh
Page 236:
104 3 Generalizing What We Learntth
Page 240:
106 3 Generalizing What We LearntTa
Page 244:
Chapter 4Stochastic Dynamical Found
Page 248:
4.4 Correlated Anomalous Diffusion
Page 252:
Page 256:
Page 260:
4.5 Stable Solutions of Fokker-Plan
Page 264:
4.6 Probabilistic Models with Corre
Page 268:
Page 272:
Page 276:
Page 280:
Page 284:
Page 288:
Page 292:
Page 296:
4.7 Central Limit Theorems 135Fig.
Page 300:
4.7 Central Limit Theorems 137See F
Page 304:
Page 308:
Page 312:
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 336:
Page 340:
Page 344:
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

Create successful ePaper yourself

Delete template?

Save as template?