The eightfold way to dissipation

TL;DR

This paper offers a comprehensive framework for understanding hydrodynamic transport consistent with thermodynamics, highlighting the predominance of adiabatic processes and the limited constraints on dissipation at leading order.

Contribution

It introduces the concept of adiabatic hydrodynamics to isolate dissipative effects and characterizes transport at all orders in the gradient expansion.

Findings

Most hydrodynamic transport is adiabatic.

Only leading-order dissipative terms are constrained by the second law.

Provides a complete classification of thermodynamically consistent hydrodynamics.

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).