CONTENTS -- Preface -- General Aspects -- Work and Heat Fluctuations in Systems with Deterministic and Stochastic Forces E. G. D. Cohen and R. Van Zon -- 1. Introduction -- 2. Non-equilibrium Fluctuation Theorems and Relations -- 2.1. Conventional Fluctuation Theorems -- 2.2. Extended Fluctuation Relations -- 2.2.1. Brownian Particle -- 2.2.2. Electric Circuits -- 3. Discussion -- Acknowledgement -- References -- Is the Entropy SQ Extensive or Nonextensive? C. Tsallis -- 1. Introduction -- 2. The case of two subsystems -- 2.1. Two independent subsystems -- 2.2. Two specially correlated subsystems -- 3. The case of three subsystems -- 3.1. Three independent subsystems -- 3.2. Three specially correlated subsystems -- 4. Enlarging the scenario -- 4.1. The case of N subsystems -- 4.2. The q case -- 4.3. Connection with the Borges-Niuanen-Le Mehaute- Wang q-product -- 5. Conclusions -- Acknowledgments -- References -- Superstatistics: Recent Developments and Applications C. Beck -- 1. Introduction -- 2. What is superstatistics? -- 3. Asymptotic behaviour for large energies -- 4. Superstatistical correlation functions -- 5. Some Applications -- References -- Two Stories Outside Boltzmann-Gibbs Statistics: Mori's Q-Phase Transitions and Glassy Dynamics at the Onset of Chaos A. Robledo, F. Baldovin and E. Mayoral -- 1. Introduction -- 2. Mori's q-phase transitions at onset of chaos -- 3. Glassy dynamics at noise-perturbed onset of chaos -- 4. Summary -- References -- Time-averages and the Heat Theorem A. Carati -- 1. Introduction -- 2. The p.d.f of the occupation number. -- 3. The Thermodynamics. -- References -- Fundamental Formulae and Numerical Evidences for the Central Limit Theorem in Tsallis Statistics H. Suyari -- 1. Q-product uniquely determined by Tsallis entropy.

2. Law of error, q-Stirling's formula, and q-multinomial coefficient in Tsallis statistics -- 2.1. Law of error in Tsallis statistics -- 2.2. Q-Stirling's formula in Tsallis statistics -- 2.3. Q-multinomial coefficient in Tsallis statistics -- 3. Numerical computations revealing the existence of the central limit theorem in Tsallis statistics -- References -- Generalizing the Planck Distribution A . M. C. Soma and C. Tsallis -- Acknowledgments -- References -- The Physical Roots of Complexity: Renewal or Modulation? P. Grigolini -- 1. Introduction -- 2. An example of complex system: the blinking quantum dots -- 3. Renewal -- 4. Modulation theory -- 5. Aging -- 6. Modulation: no aging -- 7. Concluding remarks -- References -- Nonequivalent Ensembles and Metastability H. Touchette and R. S. Ellis -- 1. Introduction -- 2. Nonequivalent ensembles -- 3. Nonequivalent ensembles and first-order phase transitions -- 4. Nonequivalent ensembles and metastability -- 5. Concluding remarks -- Acknowledgments -- References -- Applications in Physics -- Statistical Physics for Cosmic Structures L. Pietronero and F. Sylos Labini -- 1. Introduction -- 2. The problem of gravitational structure formation -- Acknowledgments -- References -- Metastability and Anomalous Behavior in the HMF Model: Connections to Nonextensive Thermodynamics and Glassy Dynamics A. Pluchino, A. Rapisarda and V: Latora -- 1. Introduction -- 2. Anomalous dynamics in the HMF model -- 2.1. Dynamical frustration and hierarchical structure -- 2.2. Nonextensive thermodynamics and HMF model -- Conclusions -- References -- Vlasov Analysis of Relaxation and Meta-equilibrium C. Anteneodo and R . O. Vallejos -- 1. Introduction -- 2. Equations of motion -- 3. First stage of relaxation -- 4. Vlasov equation -- 4.1. Lowest-order truncation -- 4.2. First-order truncation -- 4.3. Equilibrium.

4.4. Meta-equilibrium -- 5. Final remarks -- Acknowledgements -- References -- Weak Chaos in Large Conservative Systems - Infinite-range Coupled Standard Maps L. G. Moyano, A. P. Majtey and C. Tsallis -- 1. Introduction -- 2. Symplectic coupling in the coordinates -- References -- Deterministc Aging E. Barkai -- References -- Edge of Chaos of the Classical Kicked Top Map: Sensitivity to Initial Conditions S. M. Duarte Queiros and C. Tsallis -- 1. Introduction -- 2. The classical kicked top map -- References -- What Entropy at the Edge of Chaos? M. Lissia, M. Coraddu and R. Tonelli -- References -- Fractal Growth of Carbon Schwarzites G. Benedek, H. V: Tafreshi, A. Podesth and P. Milani -- 1 Introduction -- 2. Structure and Growth of Random Schwarzites -- 2.1 Topology -- 2.2 Thermodynamics -- 2.3 Serf-aflnily and Non-extemivily -- Acknowledgement -- References -- Clustering and Interface Propagation in Interacting Particle Dynamics A. Provata and V: K. Noussiou -- 1. Introduction -- 2. Bimolecular Reactive Schemes -- 3. Quadrimolecular Reactive Schemes -- 4. Interface Formation in the ZGB model -- Conclusions -- Acknowledgments -- References -- Resonant Activation and Noise Enhanced Stability in Josephson Junctions A. L. Pankratov and B. Spagnolo -- 1. Introduction and Basic Formulas -- 2. Noise induced effects -- 2.1. Resonant Activation -- 2.2. Noise Enhanced Stability -- 3. Temporal characteristics -- 4. Conclusions -- Acknowledgments -- References -- Symmetry Breaking Induced Directed Motions C.-H. Chang and T. Y. Tsong -- 1. Guidelines Introduction -- References -- Granular Media, Glasses and Thrbulence -- General Theory of Galilean-invariant Entropic Lattic Boltzmann Models B. M. Boghosian -- 1. Introduction -- 2. Discrete Kinetic Equation -- 3. Lattice Symmetries -- 4. Equilibrium Distribution Function -- 5. Hydrodynamic Equations.

6. Galilean Invariance Requirement on H -- 7. Connection with the Tsallis Entropy -- 8. Condition for Boltzmann-Gibbs Entropy -- 9. Conclusions -- Acknowledgments -- References -- Unifying Approach to the Jamming Transition in Granular Media and the Glass Transition in Thermal Systems A. Coniglio, A. De Candia, A. Fierro, M. Nicodemi, M. Pica Ciamarru and M. Tarzia -- 1. Introduction -- 2. Statistical mechanics approach to granular media -- 3. Monodisperse hard sphere model for granular materials -- 4. Mean field solution in the Bethe-Peierls approximation -- 5. Monte Carlo tap dynamics -- 6. Conclusions -- References -- Supersymmetry and Metastability in Disordered Systems I. Giardinu, A. Cavagna and G. Parisi -- 1. Introduction -- 2. Metastable states in mean-field spin glass models -- 3. Supersyrnmetry breaking and its physical interpretation -- References -- The Metastable Liquid-liquid Phase Transition: From Water to Colloids and Liquid Metals G. Franzese and H. E. Stanley -- 1. Water Anomalies and Their Interpretations -- 2. Does the Density Anomaly Imply the LL Phase Transition? -- 3. Does a LL Phase Transition Imply the Density Anomaly? -- 4. Conclusions -- References -- Optimization by Thermal Cycling A. Mobius, K. H. Hoffmann and C. Schon -- 1. Introduction -- 2. Thermal cycling algorithm -- 3. Applications -- References -- Ultra-thin Magnetic Films and the Structural Glass Transition: A Modelling Analogy S. A. Cannas, F. A. Tamarit, P. M. Gleiser and D. A. Stariolo -- 1. Introduction -- 2. A metal on metal ultra thin film model -- 3. Super cooled tetragonal liquid state -- 4. Conclusions -- Acknowledgments -- References -- Non-extensivity of Inhomogeneous Magnetic Systems M. S. Reis, V. S. Amaral, J. P. Araujo and I. S. Oliveira -- 1. Introduction -- 2. Model Description -- 3. Connections with Griffiths Singularity.

4. Connections with Experimental Results -- 5. Conclusion -- 6. Acknowledgments -- Bibliography -- Multifractal Analysis of Turbulence and Granular Flow T. Arimitsu and N. Arimitsu -- 1 Introduction -- 2 Basic Equations for Granular Flow -- 3 Multifractal Analysis -- 4 Turbulence -- 5 Granulence -- 6 Summary -- References -- Application of Superstatistics to Atmospheric Turbulence S. Rizzo and A. Rapisarda -- 1. Introduction -- 2. Statistical analysis of wind measurements -- 2.1. Correlations and power spectra -- 2.2. The superstatistics approach for wind velocity pdfs -- 3. Conclusions -- Acknowledgements -- References -- Applications in Other Sciences -- Complexity of Perceptual Processes F. T. Arecchi -- 1 Feature binding -- 1.1. Neuron synchronization -- 1.2. Perceptions, feature binding and Qualia -- 2 Homoclinic chaos, synchronization and propensity -- 3 Time code in neural information exchange -- 4 The role of the Wigner function in brain operations. -- References -- Energetic Model of Tumor Growth P. Castorina and D. Zappalh -- 1. Introduction -- 2. Cellular energetic balance and Gompertzian growth -- 3. Application to Multicellular Tumor Spheroids -- 3.1. Energetic MTS growth -- 3.2. Biomechanical eflects -- References -- Active Brownian Motion - Stochastic Dynamics of Swarms W. Ebeling and U. Erdmann -- 1. Characteristics of the dynamics of clusters and swarms -- 2. Dynamics in external fields in rigid body approximation -- 3. Dynamics of self-confined Morse clusters of driven particles -- 4. The model of harmonic swarms with global coupling -- 5. Conclusions -- References -- Complexity in the Collective Behaviour of Humans T. Vicsek -- 1. Introduction -- 2. Methods -- Examples -- Collective motion -- 3. Applications to situations involving crowds -- 4. Panic -- More practical versions -- 5. Rhythmic applause -- 6. Mexican wave.

7. Conclusions.