Large deviation theory and its main applications in

physics

## Informations pratiques

Discipline : |
Physique |

Niveau : |
Master 2 |

Semestre : |
S4a |

Crédits ECTS : |
3 |

Volume Horaire : |
18h Cours |

Responsable : |

Freddy Bouchet |

CNRS & École Normale Supérieure de Lyon, Laboratoire de Physique |

Intervenants : |

## Objectif

Large deviation theory describes rare fluctuations beyond the central limit theorem. For twenty years, this theory progressively became the main language of contemporary statistical mechanics. Its theoretical framework also became one of the basic tools of theoretical and mathematical physics besides statistical physics, with applications in field theory, condensed matter, fluid mechanics, turbulence, and also in a number of other domains of physics, theoretical chemistry or theoretical biology.

The aim of these lectures will be to give an elementary introduction to large deviation theory, aimed at studying its main physical application, at a level appropriate for graduating physicists. We will systematically motivate each chapter by relevant physical phenomena and concepts, before tintroducing the relevant formalism and theoretical tools. The main aim will be to make the students ready for original applications of their own, in physics or related sciences. The required level in theoretical physics will be a rather elementary graduate one. We will for instance deal with the following applications:

## Plan du cours

*1. *The relation between large deviation theory and thermodynamical potentials

2. Computation of free energy and entropy functions for some basic problems in statistical physics

3. The relation between large deviation theory and thermodynamical potentials

4. Computation of free energy and entropy functions for some basic problems in statistical physics

5. Gallavoti, Cohen and Evans fluctuation theorems, Crooks and Jarzynski inequality and fluctuation theorem, some of the major developments of statistical mechanics basis during the last two decades

6. The relation between kinetic theory, large deviation theory, and the irreversibility paradox

7. The use of large deviation theory for dynamical system theory (finite time Lyapunov exponents)

8. Large deviation theory and disordered systems

9. propagation, transport) and turbulence (self-organization, turbulent transport)

10. The study of multistability phenomena in a multitude of physical applications (magnetic systems, physical chemistry, polymers, turbulence, and so on)

11. Application of large deviation theory for a model of Jupiter's Great Red Spot, and several applications to climate dynamics.)

## Pré-requis

Physique statistique L3. Suggéré : Physique statistique des processus irréversibles M2

## Modalité de l'examen