First order non-Lorentzian fluids, entropy production and linear instabilities

Abstract

In this note, we investigate linear instabilities of hydrodynamics with corrections up to first order in derivatives. It has long been known that relativistic (Lorentzian) first order hydrodynamics, with positive local entropy production, exhibits unphysical instabilities. We extend this analysis to fluids with Galilean and Carrollian boost symmetries. We find that the instabilities occur in all cases, except for fluids with Galilean boost symmetry combined with the choice of macroscopic variables called Eckart frame. We also present a complete linearised analysis of the full spectrum of first order Carrollian hydrodynamics. Furthermore, we show that even in a fluid without boost symmetry present, instabilities can occur. These results provide evidence that the unphysical instabilities are symptoms of first order hydrodynamics, rather than a special feature of Lorentzian fluids.

arXiv comment9 pages of introduction and summary + 19 pages of technical details + 2 pages of appendices

References in corpus (45)

• Nonlinear Fluid Dynamics from Gravity
• From AdS/CFT correspondence to hydrodynamics
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Flow at the SPS and RHIC as a Quark Gluon Plasma Signature
• Negative local resistance caused by viscous electron backflow in graphene
• Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene
• Fluid dynamics of R-charged black holes
• New Developments in Relativistic Viscous Hydrodynamics
• Evidence for hydrodynamic electron flow in PdCoO${}_2$
• Lectures on hydrodynamic fluctuations in relativistic theories
• Hydrodynamics from charged black branes
• Gravity & Hydrodynamics: Lectures on the fluid-gravity correspondence
• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Conformal Carroll groups and BMS symmetry
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• First-order relativistic hydrodynamics is stable
• Flat Holography: Aspects of the dual field theory
• Strongly Correlated Quantum Fluids: Ultracold Quantum Gases, Quantum Chromodynamic Plasmas, and Holographic Duality
• Gauging the Carroll Algebra and Ultra-Relativistic Gravity
• Hydrodynamic gradient expansion in gauge theory plasmas
• Newtonian Gravity and the Bargmann Algebra
• Carrollian Physics at the Black Hole Horizon
• Nonlinear causality of general first-order relativistic viscous hydrodynamics
• Flat holography and Carrollian fluids
• Carroll versus Galilei Gravity
• Dynamics of Carroll Particles
• On the coupling of Galilean-invariant field theories to curved spacetime
• On the convergence of the gradient expansion in hydrodynamics
• Covariant Galilean versus Carrollian hydrodynamics from relativistic fluids
• Perfect Fluids
• Holography and hydrodynamics with weakly broken symmetries
• Incoherent transport in clean quantum critical metals
• Constructing higher-order hydrodynamics: The third order
• Revisiting non-relativistic limits
• First order and stable relativistic dissipative hydrodynamics
• Conformal non-relativistic hydrodynamics from gravity
• Short-lived modes from hydrodynamic dispersion relations
• Aspects of hot Galilean field theory
• The second law of thermodynamics from symmetry and unitarity
• Hydrodynamic Modes of Homogeneous and Isotropic Fluids
• Hydrodynamics without boosts
• Charge-Hyperscaling Violating Lifshitz hydrodynamics from black-holes
• A Hydrodynamic Description of Heavy Ion Collisions at the SPS and RHIC
• Hyperscaling-Violating Lifshitz hydrodynamics from black-holes: Part II
• Charged, conformal non-relativistic hydrodynamics

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• Newton-Cartan Submanifolds and Fluid Membranes
• Non-Lorentzian theories with and without constraints
• Recent developments in mathematical aspects of relativistic fluids
• Enstrophy without boost symmetry
• Effective field theory for hydrodynamics without boosts
• Fefferman-Graham and Bondi Gauges in the Fluid/Gravity Correspondence
• Relativistic Fluids, Hydrodynamic Frames and their Galilean versus Carrollian Avatars