Origin of the hydrodynamic Lyapunov modes

Recent studies of the Lyapunov spectrum of the hard sphere fluid reveal that there are hydrodynamic Lyapunov exponents corresponding to collective perturbations in phase space. We show that these collective perturbations are due to the conservation of certain quantities during collisions. These new conservation laws Generate new hydrodynamic fields, just as the conservation of mass, momentum, and energy Generate the density, velocity, and temperature fields. We then construct a detailed theory of the new hydrodynamic fields using a kinetic theory approach. This theory predicts several properties of the modes, but not all of them. This suggests that the underlying idea is correct, but a detailed theory must be elaborated in another way. The hydrodynamic exponents are not related in a simple way to the transport coefficients.