1. Introduction to long-range interactions

- An analytical solvable example: the mean-field Blume-Emery-Griffiths (BEG) model
- The microcanonical ensemble
- The Boltzmann entropy and the mean-field approximation
- The canonical ensemble
- Additivity
- Long-range interacting systems
- Ensemble equivalence or ensemble inequivalence

- The computation of the entropy for long-range interacting systems
- The solution of the BEG model using large deviations

- The canonical solution
- Numerical evidence of quasi-stationary states
- The microcanonical solution

- Derivation of the Klimontovich equation
- Vlasov equation: collisionless approximation of the Klimontovich equation
- The Lenard-Balescu equation
- Numerical evidence of quasi-stationary states for the HMF model
- Lynden-Bell's entropy: The principle and application to the HMF model

- Introduction
- Motivation
- Elements of fluid dynamics
- Illustration of the non additivity property
- The Onsager point vortex model
- The model
- Negative temperatures
- The statistical mechanics approach
- Deficiencies of the point vortex model
- The Robert-Sommeria-Miller theory for the 2D Euler equation
- Introduction
- The two levels approximation
- The generalization to the infinite number of levels
- Ensemble inequivalence

- Introduction
- Comparison between gravitational and electromagnetic interactions
- Equilibrium statistical mechanics of self-gravitating systems
- Loss of H-Stability
- An open system
- The extensivity issue
- The short distance issue
- The mean-field description of self-gravitating particles
- Evolution equation for the one particle distribution
- Maximization of the entropy
- Klimontovich's approach for self-gravitating particles
- Derivation of the Vlasov-Poisson equation

- Temperature, Debye shielding and quasi-neutrality
- Klimontovich's approach for particles and waves: Derivation of the Vlasov-Maxwell equations
- Bernstein-Greene-Kruskal modes

- Exercise 1: Critical temperature and the order of the phase transition for the Curie-Weiss model
- Exercice 2: Magnetization of the BEG model
- Exercice 3: Landau theory and ensemble inequivalence
- Exercice 4: The three-states Potts model
- Exercise 5: The HMF model using large deviations

Hot Plasma. Ising model combining long- with short-range interactions. (March 2016)

Synchronization. Gravitation in one dimension. (March 2017)