The eightfold way to dissipation

TL;DR

The work provides a complete framework to classify and constrain hydrodynamic transport at arbitrary gradient order under the second law by separating adiabatic from dissipative contributions. A central advance is the adiabaticity equation, solved via an eightfold classification of transport implemented by a scalar Lagrangian density ${\mathcal L}_{T}$ with a $U(1)_{\sf T}$ KMS gauge symmetry. It shows that dissipative transport is nonzero only at leading order in gradients ($k=1$), while higher-order dissipative pieces are not fixed by the second law, with hydrostatic and anomaly-induced structures fully captured by the framework. The Weyl invariant neutral fluid example demonstrates concrete constraints among second-order transport coefficients and reveals holographic relations that support a minimal-dissipation principle in strongly coupled fluids.

Abstract

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, of 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).

Figures (1)

• Figure 1: The eightfold way of hydrodynamic transport.