Abstract. I will present some recent results on large deviations for binary collision stochastic models. The paradigmatic model is the Kac’s walk, described, in the kinetic limit, by the homogeneous Boltzmann equation. Although the dynamics preserves the energy, atypical paths that violate energy conservation may occur with exponentially small probability in the number of particles. I will exhibit a few examples of atypical paths with increasing/decreasing energy, and I will show that a dynamical phase transition may occur for the asymptotics of the total number of collisions. Finally, I will discuss an entropy dissipation inequality which involves the large deviation rate function. This is a joint work with L. Bertini, D. Benedetto, E. Caglioti and D. Heydecker. Founded by the European Union - Next Generation EU.