MACROSCOPIC FLUCTUATION THEORY OF LOCAL COLLISIONAL DYNAMICS

Abstract. We explain why the macroscopic fluctuations of deterministic local collision dynamics should be characterized by a non strictly convex functional. The study of thermal conduction properties of extended lattice Hamiltonian sys-tems has received recently a lot of attention by theoretical and mathematical physi-cists alike. The first issue is simply the derivation of the Fourier law, or equivalently the heat equation. On the other hand, an impressive amount of rigorous results concerning stochastic interacting particles system has been obtained over the last decades. The diffusion equation has been derived in the hydrodynamic limit and the behaviour of the fluctuations of the macroscopic observables of the system under a space-time diffusive scaling has been derived rigorously. In particular, the shape of the large deviations functional of the current and density of particles profile has been determined [1, 2, 3, 4, 5, 6, 7, 14]. This object may be seen as the out-of-equilibrium analogue of the equilibrium thermodynamic potentials. The first example of local collision dynamics has been introduced in [8]. In that model, particles are locked in cells having a particular shape ensuring strong chaoti