• 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)