Freddy BOUCHET - ENS de Lyon and CNRS



We study fundamental aspects of statistical mechanics and statistical physics.  Our main interests include:

1) Large deviation theory applied to statistical mechanics and complex dynamical systems,

2) Kinetic theory,

3) Computation of large deviations and rare events,

4) Phase transition theory.

Large deviation theory applied to statistical mechanics and complex dynamical systems

Large deviation theory is a key framework for modern statistical mechanics. It allows to rephrase elegantly equilibrium statistical mechanics, where thermodynamic potential (entropy, free energy, and so on) then appear as large deviation rate functions. It also generalizes powerfully those concepts for non-equilibrium problems. Large deviation theory for complex dynamical systems is a key tool to understand their statistics: attractors, most probable states, typical fluctuations, rare events and extremes. We work at developing large deviation theory and its applications to statistical mechanics and complex dynamical systems through various projects:

a) Large deviation as a way to define non equilibrium thermodynamic potentials.   [.pdf]
b) Beyond large deviations: generalisation of the Eyring-Kramers transition rate formula to irreversible diffusion processes.    [.pdf]
c) Large deviations in fast–flow systems (systems with two time scales).     arXiv:1510.02227,      [.pdf]
d) Perturbative approach and Taylor series expansion of the quasi-potential for Freidlin--Wentzell type large deviations (dynamical systems with small noises).   [.pdf]
e) Beyond Freidlin-Wentzell theory: Non-classical large deviations for a noisy system with non-isolated attractors,    [.pdf]
f) Large deviation theory for the equilibrium statistical mechanics of geophysical flows. (review: F. Bouchet and A. Venaille, Physics Reports, 2009.)
g) Large deviation theory for the equilibrium statistical mechanics of systems with long range interactions. (publication: Barre-Bouchet-Dauxois-Ruffo-JStatPhys-2005.)

Some statistical physics applications of large deviations:

a) Large deviations beyond the Freidlin-Wentzell regime for front dynamics and the Allen--Cahn equation.  arXiv:1507.05577,  [.pdf]
b) Large deviations for non equilibrium systems with long range interactions, large deviations for the Shinomoto-Kuramoto model of coupled rotators.    [.pdf]
c) Large deviations and instantons for bistable turbulent systems. (publications: Bouchet--Laurie--2015 and  Bouchet--Laurie-Zaboronski--J StatPhys--2014)

Kinetic theory

Kinetic theory is a natural way to approach relaxation to equilibrium or non-equilibrium statistical mechanics of physical systems when a small parameter (often the inverse number of particle) gives a natural time scale separation. We have studied fundamental problems in kinetic theory, as well as applications in systems with long range interactions, two dimensional turbulence, and geostrophic turbulence problems. Example of past and current projects follow:

a) Kinetic theory of systems with long range interactions.  (see also the review Bouchet--Gupta--Mukamel--2010 It contains however a limited number of the problems we studied)
b) Kinetic theory of two-dimensional and geostrophic turbulence and applications to atmosphere jet dynamics.

Phase transition theory. 

To be completed