Generalized hydrodynamics revisited

Abstract: During the past decade a number of attempts to formulate a continuum description of complex states of matter have been proposed to circumvent more cumbersome many-body and simulation methods. Typically these have been quantum systems (e.g., electrons) and the resulting phenomenologies collectively often called "quantum hydrodynamics". However, there is extensive work from the past based in non-equilibrium statistical mechanics on the microscopic origins of macroscopic continuum dynamics that has not been exploited in this context. Although formally exact, its original target was the derivation of Navier-Stokes hydrodynamics for slowly varying states in space and time. The objective here is to revisit that work for the present interest in complex quantum states - possible strong degeneracy, strong coupling, and all space-time scales. The result is an exact representation of generalized hydrodynamics suitable for introducing controlled approximations for diverse specific cases, and for critiquing existing work.