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1 Equilibrium Statistical Physics |
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1 | (32) |
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1.1 Microscopic Dynamics of a Physical System |
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1 | (5) |
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1.1.1 A Particle Attached to a Spring |
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1 | (4) |
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1.1.2 Many-Particle System |
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5 | (1) |
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1.1.3 Case of Discrete Variables: Spin Models |
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5 | (1) |
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1.2 Statistical Description of an Isolated System at Equilibrium |
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6 | (6) |
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1.2.1 Notion of Statistical Description: A Toy Model |
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6 | (1) |
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1.2.2 Fundamental Postulate of Equilibrium Statistical Physics |
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7 | (1) |
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1.2.3 Computation of Q(E) and S(E): Some Simple Examples |
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8 | (2) |
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1.2.4 Distribution of Energy Over Subsystems and Statistical Temperature |
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10 | (2) |
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1.3 Equilibrium System in Contact with its Environment |
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12 | (6) |
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1.3.1 Exchanges of Energy |
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12 | (3) |
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15 | (2) |
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1.3.3 Exchanges of Particles with a Reservoir: The Grand-Canonical Ensemble |
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17 | (1) |
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18 | (9) |
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1.4.1 Example of the Ising Model |
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18 | (1) |
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1.4.2 Ising Model in Fully Connected Geometry |
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18 | (3) |
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1.4.3 Ising Model with Finite Connectivity |
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21 | (1) |
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1.4.4 Renormalization Group Approach: A Brief Introduction |
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22 | (5) |
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1.5 Disordered Systems and Glass Transition |
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27 | (6) |
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1.5.1 Disorder in Complex Systems: From Social Sciences to Spin-Glasses |
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27 | (1) |
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1.5.2 Theoretical Spin-Glass Models |
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28 | (1) |
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1.5.3 The Simplest Disordered System: The Random Energy Model |
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28 | (3) |
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31 | (2) |
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2 Non-Stationary Dynamics and Stochastic Formalism |
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33 | (26) |
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2.1 Markovian Stochastic Processes and Master Equation |
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33 | (8) |
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2.1.1 Definition of Markovian Stochastic Processes |
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33 | (2) |
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2.1.2 Master Equation and Detailed Balance |
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35 | (2) |
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2.1.3 Dynamical Increase of the Entropy |
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37 | (1) |
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2.1.4 A Simple Example: The One-Dimensional Random Walk |
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38 | (3) |
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2.2 Langevin and Fokker-Planck Equations |
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41 | (8) |
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2.2.1 Phenomenological Approach to the Langevin Equation |
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41 | (4) |
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2.2.2 Relation to Random Walks |
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45 | (2) |
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2.2.3 Fokker-Planck Equation |
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47 | (2) |
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2.3 Anomalous Diffusion and Physical Aging |
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49 | (10) |
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2.3.1 Generalized Central Limit Theorem |
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49 | (3) |
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2.3.2 Anomalous Diffusion |
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52 | (2) |
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2.3.3 Aging Dynamics and Trap Models |
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54 | (3) |
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57 | (2) |
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3 Statistical Physics of Interacting Macroscopic "Entities" |
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59 | (1) |
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3.1 Dynamics of Residential Moves |
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60 | (5) |
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3.1.1 A Simplified Version of the Schelling Model |
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61 | (1) |
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3.1.2 Equilibrium Configurations of the Model |
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61 | (2) |
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3.1.3 Condition for Phase Separation |
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63 | (2) |
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3.2 Condensation Transition |
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65 | (2) |
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3.2.1 Zero Range Process: Definition and Exact Solution |
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66 | (1) |
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3.2.2 Maximal Density and Condensation Phenomenon |
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66 | (1) |
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3.3 Synchronization Transition |
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67 | (5) |
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3.3.1 The Kuramoto Model of Coupled Oscillators |
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68 | (2) |
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3.3.2 Synchronized Steady State |
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70 | (2) |
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3.4 Collective Motion of Active Particles |
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72 | (1) |
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3.4.1 Definition of the Model |
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73 | (1) |
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3.4.2 Description Through a Boltzmann Equation |
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73 | (1) |
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3.4.3 Hydrodynamic Equations and Phase Diagram |
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74 | (3) |
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77 | |
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