Origin of the hydrodynamic Lyapunov modes - art. no. 051103

Recent studies of the Lyapunov spectrum of the hard sphere fluid reveal tha t there are "hydrodynamic" Lyapunov exponents corresponding to collective p erturbations in phase space. We show that these collective perturbations ar e due to the conservation of certain quantities during collisions. These ne w conservation laws Generate new hydrodynamic fields, just as the conservat ion of mass, momentum, and energy Generate the density, velocity, and tempe rature fields. We then construct a detailed theory of the new hydrodynamic fields using a kinetic theory approach. This theory predicts several proper ties of the modes, but not all of them. This suggests that the underlying i dea is correct, but a detailed theory must be elaborated in another way. Th e hydrodynamic exponents are not related in a simple way to the transport c oefficients.