Advanced statistical physics.

Part 1 : Out-of-equilibrium statistical physics
 

Contrary to equilibrium statistical physics, which is structured around general principles leading to the theory of ensembles, out-of-equilibrium statistical physics requires a description of the dynamics of systems, what can be achieved by a variety of approaches. The lectures introduce several concepts of the theory of stochastic processes (Markov processes, master equation, stochastic differential equation, Fokker-Planck equation). Finally we will discuss the more microscopic approach of the linear response theory.

Part 2 : Introduction to phase transitions and critical phenomena

Phase transitions originate from the competition of entropy and interaction energy, which can lead to various organisations of matter, the most remarkable aspect being that interactions of microscopic range can mediate cooperative effects responsible for ordering at a macroscopic scale.
The lectures start with a description of the liquid-gas transition, within the mean field approximation. The approach is simplified by introducing the Landau description of phase transitions, and its more elaborated form for inhomogeneous systems, the Landau-Ginzburg theory.
In a second step, the limitations of the mean field approximation are discussed, which leads to emphasize the role of scaling in phase transitions. Finally the lectures provide a brief introduction to the renormalization group (in real space).

Material:

documents can be found on the course web page http://www.lptms.universite-paris-saclay.fr/christophe_texier/enseignements/enseignements-en-master/m2-icfp-advanced-statistical-physics/

• Equilibrium statistical physics (ensemble theory)
• some concepts in probability : moments, variance and cumulants, generating function, central limit theorem 

Written exam