Classification of Hydrodynamic Transport
2442KbAbstractHydrodynamics is the low energy effective field theory of any interacting quantum theory, capturing the long wavelength fluctuations of an equilibrium Gibbs density matrix. Conventionally, one views the effective dynamics in terms of the conserved currents, which should be expressed in terms of the fluid velocity and the intensive parameters such as the temperature and chemical potential. However, not all currents allowed by symmetry are physically acceptable; one has to ensure that the second law of thermodynamics is satisfied on all physical configurations. 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 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. After completing the transport taxonomy, we go on to argue for a new symmetry principle, an Abelian gauge invariance that guarantees adiabaticity in hydrodynamics and serves as the emergent version of microscopic KMS conditions. The theory of adiabatic fluids, we speculate, provides a useful starting point for a new framework to describe non equilibrium dynamics. We outline briefly the crucial role of the proposed symmetry of gauged thermal translations in replica birkin hermes
the construction of a Schwinger Keldysh effective action that encompasses all of hydrodynamic transport.