Eightfold Classification of Hydrodynamic Dissipation

We provide a complete characterization of hydrodynamic transport consistent with the second law of thermodynamics at arbitrary orders in the gradient expansion. A key ingredient in facilitating this analysis is the notion of adiabatic hydrodynamics, which enables isolation of the genuinely dissipative parts of transport. We demonstrate that most transport is adiabatic. Furthermore, in the dissipative part, only terms at the leading order in gradient expansion are constrained to be sign definite by the second law (as has been derived before).