Constructing higher-order hydrodynamics: The third order

Abstract

Hydrodynamics can be formulated as the gradient expansion of conserved currents in terms of the fundamental fields describing the near-equilibrium fluid flow. In the relativistic case, the Navier-Stokes equations follow from the conservation of the stress-energy tensor to first order in derivatives. In this paper, we go beyond the presently understood second-order hydrodynamics and discuss the systematisation of obtaining the hydrodynamic expansion to an arbitrarily high order. As an example of the algorithm that we present, we fully classify the gradient expansion at third order for neutral fluids in four dimensions, thus finding the most general next-to-leading-order corrections to the relativistic Navier-Stokes equations in curved space-time. In doing so, we list $20$ new transport coefficient candidates in the conformal and $68$ in the non-conformal case. As we do not consider any constraints that could potentially arise from the local entropy current analysis, this is the maximal possible set of neutral third-order transport coefficients. To investigate the physical implications of these new transport coefficients, we obtain the third-order corrections to the linear dispersion relations that describe the propagation of diffusion and sound waves in relativistic fluids. We also compute the corrections to the scalar (spin-$2$) two-point correlation function of the third-order stress-energy tensor. Furthermore, as an example of a non-linear hydrodynamic flow, we calculate the third-order corrections to the energy density of a boost-invariant Bjorken flow. Finally, we apply our field theoretic results to the $\mathcal{N}=4$ supersymmetric Yang-Mills fluid at infinite 't Hooft coupling and infinite number of colours to find the values of five new linear combinations of the conformal transport coefficients.

V5: 33 pages. Typos fixed in Eqs. (5), (118) and (126). As a result, the value of the transport coefficient ${\theta }_2$ has been corrected

References in corpus (34)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Nonlinear Fluid Dynamics from Gravity
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm
• Gravity & Hydrodynamics: Lectures on the fluid-gravity correspondence
• Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation
• Local Fluid Dynamical Entropy from Gravity
• Entropy Current in Conformal Hydrodynamics
• Second order hydrodynamic coefficients from kinetic theory
• Adiabatic hydrodynamics: The eightfold way to dissipation
• Viscous plasma evolution from gravity using AdS/CFT
• Viscous hydrodynamics relaxation time from AdS/CFT
• Resolving disagreement for eta/s in a CFT plasma at finite coupling
• Thermal spectral functions of strongly coupled N=4 supersymmetric Yang-Mills theory
• Kubo Formulae for Second-Order Hydrodynamic Coefficients
• Towards an effective action for relativistic dissipative hydrodynamics
• Shear viscosity of boost invariant plasma at finite coupling
• On thermal fluctuations and the generating functional in relativistic hydrodynamics
• On the universal identity in second order hydrodynamics
• The eightfold way to dissipation
• Quasinormal spectrum and the black hole membrane paradigm
• Relativistic third-order viscous corrections to the entropy four-current from kinetic theory
• Relaxation time of a CFT plasma at finite coupling
• Thermodynamical second-order hydrodynamic coefficients
• Linearized fluid/gravity correspondence: from shear viscosity to all order hydrodynamics
• Second order hydrodynamics of a CFT plasma from boost invariant expansion
• Off-shell hydrodynamics from holography
• Effective actions for relativistic fluids from holography
• All Order Linearized Hydrodynamics from Fluid/Gravity Correspondence
• Linearly resummed hydrodynamics in a weakly curved spacetime
• Dynamics of the electric current in an ideal electron gas: a sound mode inside the quasi-particles
• Relaxation-time approximation and relativistic third-order viscous hydrodynamics from kinetic theory
• Indications of a non-trivial vacuum in the effective theory of perfect fluids

Cited by in corpus (67)

• New theories of relativistic hydrodynamics in the LHC era
• Small System Collectivity in Relativistic Hadron and Nuclear Collisions
• Causality and existence of solutions of relativistic viscous fluid dynamics with gravity
• Fluid Dynamics far from Local Equilibrium
• Generalized global symmetries and dissipative magnetohydrodynamics
• Black hole scrambling from hydrodynamics
• Many-body chaos and energy dynamics in holography
• The complex life of hydrodynamic modes
• Holography and hydrodynamics with weakly broken symmetries
• Relativistic Hydrodynamic Attractors with Broken Symmetries: Non-Conformal and Non-Homogeneous
• On the connection between hydrodynamics and quantum chaos in holographic theories with stringy corrections
• Hydrodynamics, resurgence and trans-asymptotics
• Analytical attractor and the divergence of the slow-roll expansion in relativistic hydrodynamics
• Generalised global symmetries in states with dynamical defects: the case of the transverse sound in field theory and holography
• Generalised global symmetries in holography: magnetohydrodynamic waves in a strongly interacting plasma
• Complexified quasinormal modes and the pole-skipping in a holographic system at finite chemical potential
• Shear viscosity in holography and effective theory of transport without translational symmetry
• Exact solutions and attractors of higher-order viscous fluid dynamics for Bjorken flow
• Relativistic Fluid Dynamics In and Out of Equilibrium -- Ten Years of Progress in Theory and Numerical Simulations of Nuclear Collisions
• Bounds on transport from univalence and pole-skipping
• Colloquium: Hydrodynamics and holography of charge density wave phases
• The holographic dual of a Riemann problem in a large number of dimensions
• A numerical exploration of first-order relativistic hydrodynamics
• Zoology of Solid & Fluid Holography : Goldstone Modes and Phase Relaxation
• On non-conformal kinetic theory and hydrodynamics for Bjorken flow
• Hydrodynamic gradient expansion in linear response theory
• Onset of hydrodynamics for a quark-gluon plasma from the evolution of moments of distribution functions
• Hydrodynamics from free-streaming to thermalization and back again
• Second-Order Hydrodynamics and Universality in Non-Conformal Holographic Fluids
• Conservative finite volume scheme for first-order viscous relativistic hydrodynamics
• Convergence of hydrodynamic modes: insights from kinetic theory and holography
• Inverse-Reynolds-Dominance approach to transient fluid dynamics
• Holographic Bjorken flow of a hot and dense fluid in the vicinity of a critical point
• Low frequency propagating shear waves in holographic liquids
• Effective field theory of stochastic diffusion from gravity
• First order non-Lorentzian fluids, entropy production and linear instabilities
• Holographic Turbulence in a Large Number of Dimensions
• A Lagrangian formulation of relativistic Israel-Stewart hydrodynamics
• Fluid/gravity correspondence: Second order transport coefficients in compactified D4-branes
• Is first-order relativistic hydrodynamics in general frame stable and causal for arbitrary interaction?
• Causal, stable first-order viscous relativistic hydrodynamics with ideal gas microphysics
• An effective description of momentum diffusion in a charged plasma from holography
• Third-order relativistic hydrodynamics: dispersion relations and transport coefficients of a dual plasma
• Effective holographic models for QCD: Thermodynamics and viscosity coefficients
• Resummed hydrodynamic expansion for a plasma of particles interacting with fields
• Holographic Bjorken Flow at Large-D
• Universality of anomalous conductivities in theories with higher-derivative holographic duals
• Relativistic Hydrodynamics: A Singulant Perspective
• Linearized dispersion relations in viscous relativistic hydrodynamics
• Aspects of univalence in holographic axion models
• Critical behaviour of hydrodynamic series
• The role of Weyl symmetry in hydrodynamics
• New insights into the analytic structure of correlation functions via kinetic theory
• Conformal symmetry breaking in holographic QCD
• Reconstruction of spectra and an algorithm based on the theorems of Darboux and Puiseux
• Convergence of the hydrodynamic gradient expansion in relativistic kinetic theory
• Causal third-order viscous hydrodynamics within relaxation-time approximation
• Two theorems for the gradient expansion of relativistic hydrodynamics
• Third order viscous hydrodynamics from the entropy four current
• Impacts of EMC effects on the D meson modification factor in equilibrating QGP
• Quasinormal Modes and Correlators in the Shear Channel of Spacetime-Filling Branes
• Holographic Constraints on Generalised Rivlin-Ericksen Fluid
• Hydrodynamical attractor and thermal particle production in heavy-ion collision
• Relativistic hydrodynamics with the parity anomaly
• A comparative study of different approaches for heavy quark energy loss, based on the latest experimental data
• Universal thermalization dynamics in (1+1)d QFTs
• Impact of momentum-dependent drag coefficient on energy loss of charm and bottom quarks in QGP