Complexity, Metastability And Nonextensivity (Science and Culture: Physics)

Title ......Page 3
Copyright ......Page 4
Preface ......Page 7
Contents ......Page 11
General Aspects ......Page 17
1. Introduction ......Page 19
2.1. Conventional Fluctuation Theorems ......Page 20
2.2.1. Brownian Particle ......Page 23
2.2.2. Electric Circuits ......Page 25
3. Discussion ......Page 26
References ......Page 28
1. Introduction ......Page 29
2. The case of two subsystems ......Page 32
2.2. Two specially correlated subsystems ......Page 33
3. The case of three subsystems ......Page 38
3.2. Three specially correlated subsystems ......Page 39
4.1. The case of N subsystems ......Page 41
4.2. The q case ......Page 43
4.3. Connection with the Borges-Niuanen-Le Mehaute- Wang q-product ......Page 44
5. Conclusions ......Page 46
References ......Page 47
1. Introduction ......Page 49
2. What is superstatistics? ......Page 50
3. Asymptotic behaviour for large energies ......Page 51
4. Superstatistical correlation functions ......Page 53
References ......Page 57
1. Introduction ......Page 59
2. Mori\'s q-phase transitions at onset of chaos ......Page 61
3. Glassy dynamics at noise-perturbed onset of chaos ......Page 63
References ......Page 65
1. Introduction ......Page 71
2. The p.d.f of the occupation number. ......Page 72
3. The Thermodynamics. ......Page 74
References ......Page 76
1. Q-product uniquely determined by Tsallis entropy ......Page 77
2.1. Law of error in Tsallis statistics ......Page 78
2.3. Q-multinomial coefficient in Tsallis statistics ......Page 79
3. Numerical computations revealing the existence of the central limit theorem in Tsallis statistics ......Page 80
References ......Page 81
Generalizing the Planck Distribution / A. M. C. Soma and C. Tsallis ......Page 82
References ......Page 87
1. Introduction ......Page 88
3. Renewal ......Page 89
4. Modulation theory ......Page 91
5. Aging ......Page 92
6. Modulation: no aging ......Page 93
References ......Page 95
1. Introduction ......Page 97
2. Nonequivalent ensembles ......Page 98
3. Nonequivalent ensembles and first-order phase transitions ......Page 100
4. Nonequivalent ensembles and metastability ......Page 101
Acknowledgments ......Page 102
References ......Page 103
Applications in Physics ......Page 105
1. Introduction ......Page 107
2. The problem of gravitational structure formation ......Page 114
References ......Page 116
1. Introduction ......Page 118
2. Anomalous dynamics in the HMF model ......Page 120
2.1. Dynamical frustration and hierarchical structure ......Page 121
2.2. Nonextensive thermodynamics and HMF model ......Page 124
References ......Page 127
1. Introduction ......Page 129
2. Equations of motion ......Page 130
4. Vlasov equation ......Page 131
4.1. Lowest-order truncation ......Page 132
4.2. First-order truncation ......Page 133
4.4. Meta-equilibrium ......Page 135
References ......Page 137
1. Introduction ......Page 139
2. Symplectic coupling in the coordinates ......Page 141
References ......Page 143
Deterministc Aging / E. Barkai ......Page 144
References ......Page 149
1. Introduction ......Page 151
2. The classical kicked top map ......Page 152
References ......Page 154
What Entropy at the Edge of Chaos? / M. Lissia, M. Coraddu and R. Tonelli ......Page 156
References ......Page 161
1 Introduction ......Page 162
2.1 Topology ......Page 163
2.2 Thermodynamics ......Page 167
2.3 Serf-aflnily and Non-extemivily ......Page 169
References ......Page 170
1. Introduction ......Page 172
2. Bimolecular Reactive Schemes ......Page 174
3. Quadrimolecular Reactive Schemes ......Page 177
4. Interface Formation in the ZGB model ......Page 178
References ......Page 182
1. Introduction and Basic Formulas ......Page 184
2.1. Resonant Activation ......Page 187
2.2. Noise Enhanced Stability ......Page 188
3. Temporal characteristics ......Page 189
References ......Page 193
1. Guidelines Introduction ......Page 194
References ......Page 197
Granular Media, Glasses and Thrbulence ......Page 199
1. Introduction ......Page 201
2. Discrete Kinetic Equation ......Page 202
3. Lattice Symmetries ......Page 203
4. Equilibrium Distribution Function ......Page 204
6. Galilean Invariance Requirement on H ......Page 205
7. Connection with the Tsallis Entropy ......Page 206
8. Condition for Boltzmann-Gibbs Entropy ......Page 207
Acknowledgments ......Page 208
References ......Page 209
1. Introduction ......Page 210
2. Statistical mechanics approach to granular media ......Page 211
3. Monodisperse hard sphere model for granular materials ......Page 212
4. Mean field solution in the Bethe-Peierls approximation ......Page 214
5. Monte Carlo tap dynamics ......Page 215
6. Conclusions ......Page 217
References ......Page 218
1. Introduction ......Page 220
3. Supersyrnmetry breaking and its physical interpretation ......Page 222
References ......Page 224
1. Water Anomalies and Their Interpretations ......Page 226
2. Does the Density Anomaly Imply the LL Phase Transition? ......Page 227
4. Conclusions ......Page 228
References ......Page 229
1. Introduction ......Page 231
2. Thermal cycling algorithm ......Page 232
3. Applications ......Page 233
References ......Page 235
1. Introduction ......Page 236
2. A metal on metal ultra thin film model ......Page 238
3. Super cooled tetragonal liquid state ......Page 241
4. Conclusions ......Page 244
References ......Page 245
1. Introduction ......Page 246
2. Model Description ......Page 247
3. Connections with Griffiths Singularity ......Page 248
4. Connections with Experimental Results ......Page 249
6. Acknowledgments ......Page 250
Bibliography ......Page 251
1 Introduction ......Page 252
2 Basic Equations for Granular Flow ......Page 253
3 Multifractal Analysis ......Page 254
4 Turbulence ......Page 256
5 Granulence ......Page 258
References ......Page 260
1. Introduction ......Page 262
2. Statistical analysis of wind measurements ......Page 263
2.2. The superstatistics approach for wind velocity pdfs ......Page 264
References ......Page 268
Applications in Other Sciences ......Page 269
1.1. Neuron synchronization ......Page 271
1.2. Perceptions, feature binding and Qualia ......Page 272
2 Homoclinic chaos, synchronization and propensity ......Page 274
3 Time code in neural information exchange ......Page 278
4 The role of the Wigner function in brain operations. ......Page 281
References ......Page 286
2. Cellular energetic balance and Gompertzian growth ......Page 288
3.1. Energetic MTS growth ......Page 290
References ......Page 292
1. Characteristics of the dynamics of clusters and swarms ......Page 293
2. Dynamics in external fields in rigid body approximation ......Page 294
3. Dynamics of self-confined Morse clusters of driven particles ......Page 297
4. The model of harmonic swarms with global coupling ......Page 298
5. Conclusions ......Page 301
References ......Page 302
1. Introduction ......Page 303
2. Methods ......Page 305
Collective motion ......Page 306
3. Applications to situations involving crowds ......Page 307
4. Panic ......Page 308
More practical versions ......Page 310
5. Rhythmic applause ......Page 311
6. Mexican wave ......Page 312
References ......Page 315
1. Introduction ......Page 317
2. The Bounded Confidence Model ......Page 318
2.1. Krause-Hegselmann ......Page 319
3. The Sznajd Model ......Page 320
References ......Page 321
1. Introduction ......Page 322
2. Mertonђs model ......Page 324
3. A non-Gaussian approach ......Page 325
4. Results and Discussion ......Page 327
5. Appendix ......Page 329
References ......Page 330
1. Introduction ......Page 331
2. The market response function and trade correlations ......Page 332
3. A micro-model of price fluctuations ......Page 334
4. Discussion: Critical balance of market orders vs. limit orders ......Page 337
5. Conclusion ......Page 339
References ......Page 340
1. Introduction ......Page 343
2. A correlation-based filtering procedure ......Page 344
3. Conclusions ......Page 348
References ......Page 350
1. Introduction and motivation ......Page 352
2. Path integral ......Page 353
3. Algorithms and numerical results ......Page 354
References ......Page 356
1. Introduction ......Page 357
3. Aging of aftershocks ......Page 358
4. Scaling law ......Page 361
References ......Page 364
Aging in Earthquakes Model U. Tirnakli ......Page 366
References ......Page 370
1. Introduction ......Page 371
2. The OFC model on a small-world topology ......Page 372
3. Results ......Page 374
References ......Page 376
Networks ......Page 377
1. Introduction ......Page 379
2. The Coronal Magnetic Field ......Page 381
2.1. Coronal Fields Form a Scale Free Network ......Page 382
2.2. The Model ......Page 383
2.2.1. Further predictions of the network model ......Page 384
3.1. A Unified Approach to Different Patterns of Seismic Activity ......Page 385
3.2. Relations Between Pairs of Events: The Metric ......Page 386
3.3. Directed, Weighted Networks of Correlated Earthquakes ......Page 387
3.4. The Omori Law for Earthquakes of All Magnitudes ......Page 388
References ......Page 389
1. Introduction ......Page 391
2. Comparing Apollonian and inherent structure networks ......Page 394
3. Conclusion ......Page 398
References ......Page 399
1. Introduction ......Page 401
2. The spreading of epidemics ......Page 402
ii) The urban scale ......Page 405
iii) The global scale: The airport network ......Page 406
4. Implications of network structure for epidemic dynamics ......Page 407
5. Modelling the global spread of diseases ......Page 408
6. Outlook ......Page 410
References ......Page 411
1. Introduction ......Page 413
2. Traditional Centrality Measures ......Page 414
2.1. Measures based on degree ......Page 415
2.3. Measures based on betweenness ......Page 416
3. A new idea of centrality ......Page 417
4.1. Social Networks ......Page 418
4.2. Infrastructure Networks ......Page 420
4.3. Mediators in the immune system ......Page 421
4.4. Finding Community Structures and other applications ......Page 422
References ......Page 423