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).