Large deviation theory applied to climate physics, a new frontier of statistical physics and applied mathematics.
Freddy Bouchet, ENS de Lyon et CNRS

We will review some of the recent developments in the theoretical and mathematical aspects of the non-equilibrium statistical mechanics of climate dynamics. At the intersection between statistical mechanics, turbulence, and geophysical fluid dynamics, this field is a wonderful new playground for applied mathematics. It involves large deviation theory, stochastic partial differential equations, homogenization, and diffusion Monte-Carlo algorithms. As a paradigmatic example, we will discuss trajectories that suddenly drive turbulent flows from one attractor to a completely different one, related to abrupt climate changes. More precisely we study rare transitions between attractors, in the stochastic barotropic quasigeostrophic equation. This equation models Jupiter's atmosphere jets. We discuss the mathematical justification of the use of Freidlin–Wentzell theory through averaging, compute transition rates, and instantons (most probable transition paths).