Nonextensive Statistical Mechanics

xviContents3.3 Correlations, Occupancy of Phase-Space, and Extensivity of S q .... 543.3.1 A Remark on the Thermodynamical Limit . .............. 543.3.2 The q-Product . . .................................... 613.3.3 The q-Sum......................................... 643.3.4 Extensivity of S q –EffectiveNumberofStates........... 663.3.5 Extensivity of S q –BinarySystems..................... 693.3.6 Extensivity of S q –PhysicalRealizations................ 773.4 q-Generalization of the Kullback–Leibler Relative Entropy . ....... 843.5 ConstraintsandEntropyOptimization.......................... 883.5.1 ImposingtheMeanValueoftheVariable................ 883.5.2 Imposing the Mean Value of the Squared Variable . ....... 893.5.3 Others............................................. 903.6 Nonextensive Statistical Mechanics and Thermodynamics . . ....... 903.7 About the Escort Distribution and the q-Expectation Values ....... 983.8 About Universal Constants in Physics . .........................1023.9 VariousOtherEntropicForms ................................105Part IIFoundations or Why the Theory Works4 Stochastic Dynamical Foundations of Nonextensive StatisticalMechanics .....................................................1094.1 Introduction. ...............................................1094.2 NormalDiffusion...........................................1104.3 LévyAnomalousDiffusion...................................1114.4 CorrelatedAnomalousDiffusion ..............................1114.4.1 Further Generalizing the Fokker–Planck Equation . .......1174.5 Stable Solutions of Fokker–Planck-Like Equations . ..............1174.6 Probabilistic Models with Correlations – Numericaland Analytical Approaches . . . . . . ............................ 1194.6.1 The MTG Model and Its Numerical Approach . . . . .......1204.6.2 The TMNT Model and Its Numerical Approach . . . .......1254.6.3 Analytical Approach of the MTG and TMNT Models . . . . . 1294.6.4 The RST1 Model and Its Analytical Approach . . . . .......1324.6.5 The RST2 Model and Its Numerical Approach . . . . .......1334.7 Central Limit Theorems. . ....................................1354.8 Generalizing the Langevin Equation . . .........................1444.9 Time-Dependent Ginzburg–Landau d-Dimensional O(n)Ferromagnet with n = d .................................... 1495 Deterministic Dynamical Foundations of Nonextensive StatisticalMechanics .....................................................1515.1 Low-Dimensional Dissipative Maps . . .........................1515.1.1 One-Dimensional Dissipative Maps . . ..................1515.1.2 Two-Dimensional Dissipative Maps . . ..................164