Bounds on transport from hydrodynamic stability

Abstract

It was recently shown that the dispersion relations describing singularities of retarded two-point functions in causal quantum field theories always satisfy the fundamental inequality $\mathfrak{Im}\omega \le |\mathfrak{Im}k|$, and that several rigorous bounds on transport coefficients follow directly from such inequality. Here, we prove that the same inequality, $\mathfrak{Im}\omega \le |\mathfrak{Im}k|$, is a necessary condition for a fluid theory to be covariantly stable (i.e. stable in all frames of reference). Hence, the same bounds on transport that follow from causality in quantum field theory also emerge as stability conditions within relativistic hydrodynamics. This intimate connection between bounds from causality and bounds from stability stems from the fact that covariant stability is possible only in the presence of causality. As a quick application, we show that fluids with luminal speed of sound have vanishing viscosities.

arXiv comment6 pages, 2 figures

References in corpus (10)

• New Developments in Relativistic Viscous Hydrodynamics
• New theories of relativistic hydrodynamics in the LHC era
• First-order relativistic hydrodynamics is stable
• Does stability of relativistic dissipative fluid dynamics imply causality?
• On the Causality and Stability of the Relativistic Diffusion Equation
• When the entropy has no maximum: A new perspective on the instability of the first-order theories of dissipation
• Bulk viscosity in relativistic fluids: from thermodynamics to hydrodynamics
• Unified Extended Irreversible Thermodynamics and the stability of relativistic theories for dissipation
• Stability and causality of Carter's multifluid theory
• Shock propagation and stability in causal dissipative hydrodynamics

Cited by in corpus (35)

• Theories of Relativistic Dissipative Fluid Dynamics
• Dispersion relations alone cannot guarantee causality
• Relativistic Bulk Rheology: From Neutron Star Mergers to Viscous Cosmology
• The stochastic relativistic advection diffusion equation from the Metropolis algorithm
• The Hydrohedron: Bootstrapping Relativistic Hydrodynamics
• The regime of applicability of Israel-Stewart hydrodynamics
• Universality Classes of Relativistic Fluid Dynamics: Foundations
• Causal and stable first-order chiral hydrodynamics
• Causality and classical dispersion relations
• Relativistic bulk viscous fluids of Burgers type and their presence in neutron stars
• Recent developments in mathematical aspects of relativistic fluids
• Consistent inclusion of fluctuations in first-order causal and stable relativistic hydrodynamics
• Stability of multicomponent Israel-Stewart-Maxwell theory for charge diffusion
• Universality Classes of Relativistic Fluid Dynamics: Applications
• Infinite Order Hydrodynamics: An Analytical Example
• Analytic solutions for the linearized first-order magnetohydrodynamics and implications for causality and stability
• Field redefinition and its impact in relativistic hydrodynamics
• Heat propagation in rotating relativistic bodies
• First-order relativistic hydrodynamics with an information current
• Mapping GENERIC hydrodynamics into Carter's multifluid theory
• Dispersion relations of relativistic radiation hydrodynamics
• Causality Criteria from Stability Analysis at Ultra-High Boost
• Noncovariant parabolic theories of relativistic diffusion
• Causality constraints on radiative transfer
• Anisotropic linear waves and breakdown of the momentum expansion in spin magnetohydrodynamics
• Causal and Stable Superfluid Hydrodynamics
• Extending Israel-Stewart theory: Causal bulk viscosity at large gradients
• The quasi-normal modes of relativistic Fokker-Planck kinetic theory
• How Lorentz boosts reshape relaxation spectra
• The initial data of effective field theories of relativistic viscous fluids and gravity
• Solitons and singularities in relativistic ultrastiff fluids
• Thermoelectric Conduction in General Relativity: A Causal, Stable, and Well Posed Theory
• Lorentz-boosted diffusion: initial value formulation and exact solutions
• The diffusion equation is compatible with special relativity
• Thermodynamic stability of superflows in General Relativity and Newtonian gravity