Non-dissipative hydrodynamics: Effective actions versus entropy current

TL;DR

This paper explores non-dissipative hydrodynamics through effective actions, identifying specific transport coefficients and contrasting them with entropy current formalism, revealing a mismatch in parameter spaces.

Contribution

It systematically constructs non-dissipative hydrodynamics from an effective field theory perspective and compares it with entropy current constraints, highlighting differences in parameter families.

Findings

Identifies five second-order transport coefficients from effective action.

Finds a seven-parameter family of non-dissipative fluids from entropy current analysis.

Highlights a mismatch between effective action and entropy current parameter spaces.

Abstract

While conventional hydrodynamics incorporating dissipative effects is hard to derive from an action principle, it is nevertheless possible to construct classical actions when the dissipative terms are switched off. In this note we undertake a systematic exploration of such constructions from an effective field theory approach and argue for the existence of non-trivial second order non-dissipative hydrodynamics involving pure energy-momentum transport. We find these fluids to be characterized by five second-order transport coefficients based on the effective action (a three parameter family is Weyl invariant). On the other hand since all flows of such fluids are non-dissipative, they entail zero entropy production; one can therefore understand them using the entropy current formalism which has provided much insight into hydrodynamic transport. An analysis of the most general stress tensor with zero entropy production however turns out to give a seven parameter family of non-dissipative hydrodynamics (a four parameter sub-family being Weyl invariant). The non-dissipative fluids derived from the effective action approach are a special case of the fluid dynamics constrained by conservation of the entropy current. We speculate on the reasons for the mismatch and potential limitations of the effective action approach.