  We provide a complete solution to hydrodynamic transport at all orders in the
gradient expansion compatible with the second law constraint. The key new
ingredient we introduce is the notion of adiabaticity, which allows us to take
hydrodynamics off-shell. Adiabatic fluids are such that off-shell dynamics of
the fluid compensates for entropy production. The space of adiabatic fluids is
quite rich, and admits a decomposition into seven distinct classes. Together
with the dissipative class this establishes the eightfold way of hydrodynamic
transport. Furthermore, recent results guarantee that dissipative terms beyond
leading order in the gradient expansion are agnostic of the second law. While
this completes a transport taxonomy, we go on to argue for a new symmetry
principle, an Abelian gauge invariance that guarantees adiabaticity in
hydrodynamics. We suggest that this symmetry is the macroscopic manifestation
of the microscopic KMS invariance. We demonstrate its utility by explicitly
constructing effective actions for adiabatic transport. The theory of adiabatic
fluids, we speculate, provides a useful starting point for a new framework to
describe non-equilibrium dynamics, wherein dissipative effects arise by
Higgsing the Abelian symmetry.
