# Bruno Marcos - Universite Côte d’Azur, CNRS UMR 7351, LJAD, France - Keywords: Statistical Physics, Long range interactions

In Statistical Physics, we call systems with long range interactions those in which all the particles interact significantly. There are many such systems in nature: self-gravitating systems as galaxies, globular clusters or the large scale structure of the Universe, cold trapped atoms, colloids at surface interfaces, active particles, etc. The long range interaction nature of these systems results in the apparition of "exotic" collective effects compared with short range systems. They have different manifestations: formation of Quasi-Stationary States via the mechanism of "violent relaxation" (such as a galaxy, which is a quasi-stable structure but completely out of thermodynamic

equilibrium), "collisional" slow relaxation towards thermodynamic equilibrium in a time scaling with the number of particles, apparition of negative specific heat at thermodynamic equilibrium, etc.

In this contribution I will focus on the process of "collisional" slow relaxation of a long range system towards thermodynamic equilibrium. An example of such process is the evaporation of stars in a galaxy or a globular cluster. This process is driven by the finiteness of the number of particles, which causes fluctuations ("noise") in the (mean-field) potential generated by the system. The effect of these fluctuations can be modeled, as it is usually done in Statistical Physics, through a Fokker-Planck or Langevin equation. There are however two important difficulties: (i) the noise has to be modeled very precisely taking into account accurately the orbit of each particle and (ii) the motion of the particles perturbs in turn the mean-field potential. It results in general in very difficult perturbative calculations. I will present exact calculations of diffusion coefficients for spatially inhomogeneous systems, performed for a simplified one-dimensional long range model, the Hamiltonian Mean Field model. This work has been published in Phys. Rev. E 95, 022111 (2017).