Perturbative approaches in relativistic kinetic theory and the emergence of first-order hydrodynamics

Abstract

Hydrodynamics can be formulated in terms of a perturbative series in derivatives of the temperature, chemical potential, and flow velocity around an equilibrium state. Different formulations for this series have been proposed over the years, which consequently led to the development of various hydrodynamic theories. In this work, we discuss the relativistic generalizations of the perturbative expansions put forward by Chapman and Enskog, and Hilbert, using general matching conditions in kinetic theory. This allows us to describe, in a comprehensive way, how different out-of-equilibrium definitions for the hydrodynamic fields affect the development of the hydrodynamic perturbative series. We provide a perturbative method for systematically deriving the hydrodynamic formulation recently proposed by Bemfica, Disconzi, Noronha, and Kovtun (BDNK) from relativistic kinetic theory. The various transport coefficients that appear in BDNK (at first-order) are explicitly computed using a new formulation of the relaxation time approximation for the Boltzmann equation. Assuming Bjorken flow, we also determine the hydrodynamic attractors of BDNK theory and compare the overall hydrodynamic evolution obtained using this formulation with that generated by the Israel-Stewart equations of motion and also kinetic theory.

arXiv comment36 pages, 8 figures

References in corpus (49)

• Nonlinear Fluid Dynamics from Gravity
• Elliptic and triangular flow in event-by-event (3+1)D viscous hydrodynamics
• Derivation of transient relativistic fluid dynamics from the Boltzmann equation
• Transport coefficients in high temperature gauge theories: (I) Leading-log results
• Lectures on hydrodynamic fluctuations in relativistic theories
• Effective Kinetic Theory for High Temperature Gauge Theories
• New theories of relativistic hydrodynamics in the LHC era
• Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation
• First-order relativistic hydrodynamics is stable
• Symmetry constraints on generalizations of Bjorken flow
• Causality and existence of solutions of relativistic viscous fluid dynamics with gravity
• QCD thermalization: Ab initio approaches and interdisciplinary connections
• Fluid Dynamics far from Local Equilibrium
• Nonlinear causality of general first-order relativistic viscous hydrodynamics
• Does stability of relativistic dissipative fluid dynamics imply causality?
• Bulk Viscosity Effects in Event-by-Event Relativistic Hydrodynamics
• The anisotropic non-equilibrium hydrodynamic attractor
• A new exact solution of the relativistic Boltzmann equation and its hydrodynamic limit
• Stability and Causality in relativistic dissipative hydrodynamics
• Stable and causal relativistic Navier-Stokes equations
• Derivation of fluid dynamics from kinetic theory with the 14--moment approximation
• Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation
• Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow
• Novel Relaxation Time Approximation to the Relativistic Boltzmann Equation
• Nonlinear Constraints on Relativistic Fluids Far From Equilibrium
• Non-resistive dissipative magnetohydrodynamics from the Boltzmann equation in the 14-moment approximation
• Resistive dissipative magnetohydrodynamics from the Boltzmann-Vlasov equation
• First order and stable relativistic dissipative hydrodynamics
• Non-equilibrium attractor in high-temperature QCD plasmas
• Relativistic hydrodynamics - causality and stability
• Exact hydrodynamic attractor of an ultrarelativistic gas of hard spheres
• Hydrodynamic attractors in heavy ion collisions: a review
• When the entropy has no maximum: A new perspective on the instability of the first-order theories of dissipation
• Analytic solution of the Boltzmann equation in an expanding system
• Hydrodynamic attractor and the fate of perturbative expansions in Gubser flow
• Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow
• A numerical exploration of first-order relativistic hydrodynamics
• General-relativistic hydrodynamics of non-perfect fluids: 3+1 conservative formulation and application to viscous black-hole accretion
• Transient Relativistic Fluid Dynamics in a General Hydrodynamic Frame
• Non-conformal attractor in boost-invariant plasmas
• Stable First-order Particle-frame Relativistic Hydrodynamics for Dissipative Systems
• On attractor and fixed points in Bjorken flows
• Linear stability of Israel-Stewart theory in the presence of net-charge diffusion
• Pre-hydrodynamic evolution and its signatures in final-state heavy-ion observables
• Dissipative Magnetohydrodynamics for Non-Resistive Relativistic Plasmas
• Conservative finite volume scheme for first-order viscous relativistic hydrodynamics
• Causality and stability in relativistic viscous non-resistive magneto-fluid dynamics
• Is first-order relativistic hydrodynamics in general frame stable and causal for arbitrary interaction?
• Derivation of Covariant Dissipative Fluid Dynamics in the Renormalization-group Method

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• Theories of Relativistic Dissipative Fluid Dynamics
• Causal first-order hydrodynamics from kinetic theory and holography
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• Hydrodynamic theories for a system of weakly self-interacting classical ultra-relativistic scalar particles: microscopic derivations and attractors
• Causal, stable first-order viscous relativistic hydrodynamics with ideal gas microphysics
• Causal and stable first-order chiral hydrodynamics
• Recent developments in mathematical aspects of relativistic fluids
• Cosmological consequences of first-order general-relativistic viscous fluid dynamics
• Far-from-equilibrium kinetic dynamics of $\lambda {\varphi }^4$ theory in an expanding universe
• Infinite Order Hydrodynamics: An Analytical Example
• Causality Criteria from Stability Analysis at Ultra-High Boost
• Confinement/deconfinement at low temperatures and rotation in the exact soft wall model
• Deformations of the AdS-Schwarzschild black brane and the shear viscosity of the quark-gluon plasma
• Relaxation Time Approximation for a multi-species relativistic gas
• A general relativistic kinetic theory approach to linear transport in generic hydrodynamic frame
• Phase transitions at high and low densities for a rotating QCD matter from holography
• Transport and response coefficients in second-order dissipative relativistic hydrodynamics with quantum corrections: probing the quark-gluon plasma