In physics, and more particularly in statistical mechanics, these nonlinear evolution equations are often used to describe the statistical behavior of microscopic interacting particles in a fluid or in some condensed matter. In this context, the random evolution of a virtual fluid or a gas particle is represented by McKean-Vlasov diffusion processes, reaction–diffusion systems, or Boltzmann type collision processes. As its name indicates, the mean field particle model represents the collective behavior of microscopic particles weakly interacting with their occupation measures. The macroscopic behavior of these many-body particle systems is encapsulated in the limiting model obtained when the size of the population tends to infinity. Boltzmann equations represent the macroscopic evolution of colliding particles in rarefied gases, while McKean Vlasov diffusions represent the macroscopic behavior of fluid particles and granular gases.