Adiabatic hydrodynamics: The eightfold way to dissipation

TL;DR

This paper develops a comprehensive classification of hydrodynamic transport at all orders, introducing the concept of adiabaticity and a new symmetry principle to better understand non-equilibrium fluid dynamics.

Contribution

It introduces the notion of adiabaticity in hydrodynamics, classifies transport into eight classes, and proposes an Abelian gauge invariance as a fundamental symmetry.

Findings

Complete solution to hydrodynamic transport at all gradient orders.

Identification of seven classes of adiabatic fluids plus dissipative class.

Construction of effective actions demonstrating adiabatic transport.

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.