Constraints on Superfluid Hydrodynamics from Equilibrium Partition Functions

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.

46 pages

References in corpus (5)

• Nonlinear Fluid Dynamics from Gravity
• Gravity & Hydrodynamics: Lectures on the fluid-gravity correspondence
• Towards hydrodynamics without an entropy current
• Relativistic Hydrodynamics with General Anomalous Charges
• Hydrodynamics in 1+1 dimensions with gravitational anomalies

Cited by in corpus (39)

• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• Thermodynamics, gravitational anomalies and cones
• Anomaly inflow and thermal equilibrium
• Chiral conductivities and effective field theory
• A Strongly Coupled Anisotropic Fluid From Dilaton Driven Holography
• Magnetohydrodynamics as superfluidity
• Aspects of hot Galilean field theory
• Chiral hydrodynamics in strong external magnetic fields
• Entropy Current from Partition Function: One Example
• Entropy current and equilibrium partition function in fluid dynamics
• How Fluids Bend: the Elastic Expansion for Higher-Dimensional Black Holes
• Hydrodynamics, spin currents and torsion
• Transport and hydrodynamics in the chiral limit
• Thermodynamics of polarized relativistic matter
• Anomalies and the Helicity of the Thermal State
• Damping of Pseudo-Goldstone Fields
• An Action for and Hydrodynamics from the improved Large D membrane
• New Transport Properties of Anisotropic Holographic Superfluids
• Surface transport in plasma-balls
• A theory for non-Abelian superfluid dynamics
• Ideal fracton superfluids
• Anomalous Transport in Holographic Chiral Superfluids via Kubo Formulae
• On the surface of superfluids
• Two dimensional hydrodynamics with gauge and gravitational anomalies
• Dual Dressed Black Holes as the end point of the Charged Superradiant instability in $\mathcal{N}=4$ Yang Mills
• Non-Abelian Anomalous (Super)Fluids in Thermal Equilibrium from Differential Geometry
• Holographic Thermal Helicity
• Parity violating quantum kinetic theory in (2+1)-dimensions
• Entropy current in two dimensional anomalous hydrodynamics and a bound on the sum of the response parameters
• Non-vanishing normal density in cold holographic superfluids
• Anomalous Currents and Constitutive Relations of a Chiral Hadronic Superfluid
• First Order Galilean Superfluid Dynamics
• Universal chiral conductivities for low temperature holographic superfluids
• Chiral asymmetry in cold QED plasma in a strong magnetic field
• Superfluid Kubo Formulas from Partition Function
• Vacuum condition and the relation between response parameter and anomaly coefficient in (1+3) dimensions
• Causal and Stable Superfluid Hydrodynamics
• Second order Galilean fluids & Stokes' law
• Anomalous hydrodynamics with dyonic charge