Onsager's theorem and higher-order hydrodynamic equations

Hydrodynamic equations of higher order, such as Burnett's equations, do not satisfy Onsager's theorem in its usual form. The reason for this is investigated, and is found to be related to the existence of "initial slip." A recent application of Onsager's theorem to the number of propagating hydrodynamic modes is generalized to apply to linear hydrodynamic equations of any order.