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On the Causality and Stability of the Relativistic Diffusion Equation

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arxiv cond-mat/0010276 v1 pith:GHJRVTYG submitted 2000-10-19 cond-mat.stat-mech

Peter Kostaedt , Mario Liu This is my paper
classification cond-mat.stat-mech
keywords relativisticdiffusionequationmathematicalargumentcausalityconditionsemerge
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This paper examines the mathematical properties of the relativistic diffusion equation. The peculiar solution which Hiscock and Lindblom identified as an instability is shown to emerge from an ill-posed initial value problem. These do not meet the mathematical conditions required for realistic physical problems and can not serve as an argument against the relativistic hydrodynamics of Landau and Lifshitz.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Lorentzian geometry of relaxation

    nucl-th 2026-07 accept novelty 8.0 of 10

    Causality forces purely relaxational dispersion relations to follow spacelike trajectories on the Lorentzian {iω,ik} plane, producing universal bounds on diffusivity, viscosity, time-dilation deviations, and hydrodyna...

  2. Lorentz-boosted diffusion: initial value formulation and exact solutions

    math-ph 2026-02 conditional novelty 7.0 of 10

    Lorentz-boosted diffusion becomes a well-posed initial-value problem on a band-limited (Paley-Wiener) function space, with an exact closed-form Shannon-Whittaker Green function.

  3. The diffusion equation is compatible with special relativity

    gr-qc 2026-01 conditional novelty 6.0 of 10

    A relativistic kinetic theory (Vlasov–Fokker–Planck) has an exact subsector whose particle density evolves by Fick's law at all wavelengths, reconciling diffusion with causality and stability.

  4. Noncovariant parabolic theories of relativistic diffusion

    gr-qc 2025-05 accept novelty 6.0 of 10

    A quantitative analysis shows that observer-dependent effects in a new relativistic diffusion theory scale like the square root of time, slower than standard truncation errors, yet remain finite as speeds approach light.

  5. The initial data of effective field theories of relativistic viscous fluids and gravity

    gr-qc 2026-02 conditional novelty 5.0 of 10

    Initial data for the unphysical modes in well-posed EFTs should be fixed by order reduction, which suppresses fast modes without altering the equations of motion.

  6. Relativistic Dispersion Spectra across Lorentz boosted frames: Spurious modes and the enigma of causality

    hep-th 2025-12 conditional novelty 5.0 of 10

    Rest-frame dispersion modes can be mapped into Lorentz-boosted frames through a parametric re-parametrization; the boost-generated 'spurious' roots appear exactly when the mode count is not conserved, which the author...

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