Hydrodynamic limit for the velocity-flip model

International audienceWe review the proof of the hydrodynamic limit for the velocity-flip modelwhich is given in [12]. We study the diffusive scaling limit for a chain of N coupledharmonic oscillators. In order to provide the system with good ergodic properties,we perturb the Hamiltonian dynamics with random flips of velocities, so that theenergy is still conserved. We derive the hydrodynamic equations by estimating therelative entropy with respect to the local equilibrium state modified by a correctionterm