Abstract
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.
Highlights
Hydrodynamics, as is well known, is the universal long-wavelength effective description of near-equilibrium dynamics of interacting quantum systems
While many attempts have been made to distill the essentials of the theory and derive the low energy dynamics following rules of effective field theory, it is perhaps fair to say that to date a completely autonomous theory of hydrodynamics remains in absentia
To motivate the study of adiabatic fluids, let us ask the following question: “what is the most convenient way to implement the second law of thermodynamics, which apriori is stated as an inequality, in practice?” As we discussed before the conventional current-algebraic approach is to work on-shell by classifying independent tensors, but this is limiting from the point of view of constructing an action principle
Summary
Hydrodynamics, as is well known, is the universal long-wavelength effective description of near-equilibrium dynamics of interacting quantum systems. To motivate the study of adiabatic fluids, let us ask the following question: “what is the most convenient way to implement the second law of thermodynamics, which apriori is stated as an inequality, in practice?” As we discussed before the conventional current-algebraic approach is to work on-shell by classifying independent tensors, but this is limiting from the point of view of constructing an action principle. This allows us to give an alternate proof of the theorem, classifying dissipative transport coefficients into those constrained by the second law, and those that are agnostic to entropy production. 12A clue to the existence of such a structure is provided by the analysis of hydrostatic partition functions satisfying the Euclidean consistency condition in the presence of gravitational anomalies [13]
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