Constraints on Superfluid Hydrodynamics from Equilibrium Partition Functions

TL;DR

This paper derives constraints on relativistic superfluid hydrodynamics by analyzing the equilibrium partition function and effective action, showing these constraints align with thermodynamic principles.

Contribution

It introduces a method to derive superfluid hydrodynamic constraints from an effective action approach, linking microscopic symmetries to macroscopic transport coefficients.

Findings

Partition function generated by a 3D Euclidean effective action.

Constraints on constitutive relations match those from the second law of thermodynamics.

First-order derivative expansion constraints are explicitly characterized.

Abstract

Following up on recent work in the context of ordinary fluids, we study the equilibrium partition function of a 3+1 dimensional superfluid on an arbitrary stationary background spacetime, and with arbitrary stationary background gauge fields, in the long wavelength expansion. We argue that this partition function is generated by a 3 dimensional Euclidean effective action for the massless Goldstone field. We parameterize the general form of this action at first order in the derivative expansion. We demonstrate that the constitutive relations of relativistic superfluid hydrodynamics are significantly constrained by the requirement of consistency with such an effective action. At first order in the derivative expansion we demonstrate that the resultant constraints on constitutive relations coincide precisely with the equalities between hydrodynamical transport coefficients recently derived from the second law of thermodynamics.