High Energy Physics - Theory · arXiv:2308.02928 v2 · submitted 5 Aug 2023
Causal and stable first-order chiral hydrodynamics
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“Furthermore, our analysis yields, to the best of our knowledge, the first theory of viscous chiral hydrodynamics proven to be causal and stable.”
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Abstract
We derive the set of inequalities that is necessary and sufficient for nonlinear causality and linear stability of first-order relativistic hydrodynamics with either a U(1)V conserved current or a U(1)A current with a chiral anomaly or both. Our results apply to generic hydrodynamic frames in which no relations among the transport parameters are imposed. Furthermore, our analysis yields, to the best of our knowledge, the first theory of viscous chiral hydrodynamics proven to be causal and stable. We find that causality demands the absence of vorticity-induced heat flux, forcing a departure from the thermodynamic frame in the chiral case. The inequalities for causality and stability define a hypervolume in the space of transport parameters, wherein each point corresponds to a consistent formulation. Notably, causality is determined by just three combinations of transport parameters. We present our results in a form amenable to numerical hydrodynamic simulations.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 1.00
What the abstract itself states, as probabilities: claims first 0.93 · states limitation 0.25 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.65 · compares with prior results 0.41 · mentions code or data availability 0.03
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v2). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| We derive the set of inequalities that is necessary and sufficient for nonlinear causality and linear stability of first-order relativistic hydrodynamics with either a $U(1)_V$ conserved current or a $U(1)_A$ current with a chiral anomaly or both. | contribution 0.77 | 0.96 | 0.51 | asserted 1.00 |
| Our results apply to generic hydrodynamic frames in which no relations among the transport parameters are imposed. | contribution 0.59 | 0.66 | 0.05 | asserted 1.00 |
| Furthermore, our analysis yields, to the best of our knowledge, the first theory of viscous chiral hydrodynamics proven to be causal and stable. | result 0.51 | 0.94 | 0.55 | asserted 1.00 |
| We find that causality demands the absence of vorticity-induced heat flux, forcing a departure from the thermodynamic frame in the chiral case. | result 0.89 | 0.96 | 0.15 | asserted 1.00 |
| The inequalities for causality and stability define a hypervolume in the space of transport parameters, wherein each point corresponds to a consistent formulation. | result 0.84 | 0.92 | 0.17 | asserted 1.00 |
| Notably, causality is determined by just three combinations of transport parameters. | result 0.95 | 0.92 | 0.14 | asserted 1.00 |
| We present our results in a form amenable to numerical hydrodynamic simulations. | contribution 0.72 | 0.89 | 0.04 | asserted 1.00 |
What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,575 input tokens.
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Cited by 4 Pith papers
Reviewed papers on Pith that cite this one. The full citation record
- Mathematical foundations and numerical simulations of BDNK hydrodynamics: from heavy-ion collisions to astrophysics nucl-th · Nov 2026
- Nonlinear Causality and Strong Hyperbolicity of Einstein-Israel-Stewart Theories of Transient Relativistic Fluid Dynamics nucl-th · Jul 2026
- Stable and causal frames for BDNK hydrodynamics hep-th · Oct 2026
- Theories of Relativistic Dissipative Fluid Dynamics nucl-th · Nov 2023
How the literature uses it
15 arXiv papers cite this in 18 sentences
Papers whose main result relates to this one's
States the same result 1 paper
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This is the first theory of first-order chiral hydrodynamics suitable for numerical simulations.
A new causal and stable theory of viscous chiral hydrodynamics · 0.97
Papers citing it · 14 sentences without a confident label
Compares with it 1 paper
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Moreover, the conditions found in [ref] are expressed in terms of completely generic transport coefficients, while in this work we restrict to the on-shell EFT constitutive-relations, namely choices that make the non-equilibrium terms proportional to the evolution equation of the ideal fluid, as done in [ref] .
A strongly hyperbolic viscous relativistic hydrodynamics theory with first-order charge current · Introduction · 0.90
Cites it as background 3 papers
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Similar theoretical explorations employing linear mode analysis have also been conducted in the context of relativistic magneto-hydrodynamics [ref] and chiral hydrodynamics [ref] .
Stability and causality of rest frame modes in second-order spin hydrodynamics · Introduction · 0.85
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One is demanded to perform more analyses when including more conserved charges such as a vector charge [ref] , magnetic field [ref] , axial charge [ref] , and/or spin [ref] .
Analytic solutions for the linearized first-order magnetohydrodynamics and implications for causality and stability · Introduction · 0.83
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There have also been several important developments in this direction, extending, refining and validating the framework in various contexts [ref] .
Relativistic BDNK MHD Evolution in a Boost-Invariant Medium and Its Impact on Dilepton Production · Introduction · 0.84
What it cites · 86 sentences without a confident label
Builds on 1 paper
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This theory can be obtained from the one set out in Sec. [ref] by making the following modifications (generalizing Ref. [ref] to a generic hydrodynamic frame).
Hydrodynamics with Triangle Anomalies · Chiral BDNK hydrodynamics · 0.99
Uses the method or tool of 2 papers
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Here, instead, following Ref. [ref] , it is more convenient to leave $_μT^μν=0$ alone and to apply the operator $u^λ_λ$ twice to the constraint equation $u^μu_μ= -1$, yielding [equation] as an additional equation of motion.
Nonlinear causality of general first-order relativistic viscous hydrodynamics · Causality · 0.99
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Following [ref] , we preemptively change variables from $T$ and $μ$ to $$ and $n$, as doing so will simplify the analysis of stability (see Sec. [ref]).
First-Order General-Relativistic Viscous Fluid Dynamics · Change of variables · 0.91
Compares with 2 papers
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The first class of frames, where $_3 = π_3 = θ_3=0$, is closely analogous to the class $_3 = π_3 = θ_3 = 0$ already studied in detail by Ref. [ref] , because the determinant factorizes in the same way.
Stable and causal relativistic Navier-Stokes equations · Causality · 0.92
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An analogous result was previously obtained for ideal chiral hydrodynamics [ref] .
Challenges in Solving Chiral Hydrodynamics · Causality and stability · 0.89
Cites as background 37 papers
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While chiral (or anomalous) hydrodynamics [ref] , the hydrodynamic theory which incorporates the effect of quantum anomalies, has provided crucial understanding of how these anomalies manifest at the macroscopic level in fluids, there remain fundamental issues that must be considered when investigating the initial-value problem in such theories [ref] .
Fluid dynamics of R-charged black holes · Introduction · 0.93
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While chiral (or anomalous) hydrodynamics [ref] , the hydrodynamic theory which incorporates the effect of quantum anomalies, has provided crucial understanding of how these anomalies manifest at the macroscopic level in fluids, there remain fundamental issues that must be considered when investigating the initial-value problem in such theories [ref] .
Hydrodynamics from charged black branes · Introduction · 0.93
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While chiral (or anomalous) hydrodynamics [ref] , the hydrodynamic theory which incorporates the effect of quantum anomalies, has provided crucial understanding of how these anomalies manifest at the macroscopic level in fluids, there remain fundamental issues that must be considered when investigating the initial-value problem in such theories [ref] .
Anomalous Transport from Kubo Formulae · Introduction · 0.93
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