Laboratoire de Physique Théorique
Toulouse - UMR 5152

Long-range interacting systems include gravitational systems, plasma in the low density limit, two-dimensional and geophysical fluid models.

In many physical context, long-range interacting systems are found to be out of equilibrium because of external drving. Examples come from climate dynamics, plasma physics and, recently, experimental setups with cold-atoms driven by laser light.

Geophysical flows, for example, are characterised by their self-organisation into large scale coherent structures such as jet-streams, cyclones and anti-cyclones. The description of these structures, of their evolution and of extreme events they undergone (such as the sudden switch of the system between multiple attractors) are outstanding problems at the interface between climate science and statistical mechanics.

In order to address the description of driven long-range interacting systems in a theoretical way, we concentrate in this talk on models as simple as possible that still retain the following two main characteristics : non-local (i.e. long-range) nature of the interactions and broken detailed balance (i.e. non-equilibrium dynamics).

We present results both for particle systems and quasi two-dimensional flows and we show that their dynamics can be described very accurately in the limit where there is a separation of time-scales between the evolution of the mean state and the evolution of the fluctuations around it. The main theoretical tools developed are kinetic theory and large deviations techniques : the accuracy of the results obtained will be compared to direct numerical simulations. Ongoing work and perspectives on a combination of kinetic theory and large deviations theory to describe multistability in a very performant way will also be described.