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arxiv: 2606.01805 · v1 · pith:CEKWUEFUnew · submitted 2026-06-01 · ⚛️ nucl-th · hep-th

Hydrodynamics without a relaxation gap: memory effects, nonlocality, and superdiffusion

Lorenzo Gavassino , Sukanya Mitra , Rajeev Singh This is my paper

Pith reviewed 2026-06-28 12:24 UTC · model grok-4.3

classification ⚛️ nucl-th hep-th
keywords relativistic hydrodynamicsrelaxation time approximationmemory effectsnonlocalitysuperdiffusiongradient expansionnon-hydrodynamic modesRTA matching frame
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The pith

Sufficiently singular relaxation spectra invalidate ordinary diffusion, replacing it with superdiffusion via nonlocal relations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines a model of relativistic particles in a background medium where the relaxation time depends on energy and grows without any upper bound. This creates persistent memory from the gapless non-hydrodynamic sector that blocks the formation of local hydrodynamic descriptions. The full gradient expansion diverges for most flows, including Fourier modes, and resummations keep an infinite number of slow non-hydrodynamic modes active. When the relaxation spectrum becomes singular enough, the diffusivity diverges and ordinary diffusion no longer describes the late-time behavior. The dynamics instead follow superdiffusive evolution governed by intrinsically nonlocal constitutive relations.

Core claim

In the RTA matching frame, a simple model of relativistic particles propagating through a background medium with an energy-dependent relaxation time unbounded from above shows that long-term memory obstructs local hydrodynamics in systems with a gapless non-hydrodynamic sector. The full gradient expansion is generically divergent in most flows even for Fourier modes, and any resummation retains an infinite set of slow non-hydrodynamic degrees of freedom. This divergence reflects a breakdown of hydrodynamic locality caused by persistent non-hydrodynamic memory. Sufficiently singular relaxation spectra invalidate ordinary diffusion itself, with the diffusivity diverging and late-time dynamics

What carries the argument

The energy-dependent relaxation time unbounded from above in the relaxation time approximation (RTA) matching frame, which generates persistent non-hydrodynamic memory and prevents locality.

If this is right

  • The gradient expansion diverges even for Fourier modes in most flows.
  • Resummation of the expansion retains an infinite set of slow non-hydrodynamic degrees of freedom.
  • Hydrodynamic locality breaks down due to persistent non-hydrodynamic memory.
  • Ordinary diffusion is invalidated when relaxation spectra are sufficiently singular.
  • Diffusivity diverges and late-time dynamics become superdiffusive under nonlocal constitutive relations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The breakdown may extend to other systems whose non-hydrodynamic sector lacks a gap.
  • Hydrodynamic modeling in such regimes requires retaining nonlocal terms rather than local approximations.
  • Numerical implementations of hydrodynamics could test the transition to superdiffusion by varying the relaxation spectrum.
  • The result suggests that memory effects can dominate transport whenever relaxation times lack an upper bound.

Load-bearing premise

The model assumes an energy-dependent relaxation time that is unbounded from above in a simple relativistic particle system.

What would settle it

A direct calculation of the late-time transport in this RTA model that yields a finite diffusivity and recovers ordinary diffusion despite the singular spectrum.

Figures

Figures reproduced from arXiv: 2606.01805 by Lorenzo Gavassino, Rajeev Singh, Sukanya Mitra.

Figure 1
Figure 1. Figure 1: FIG. 1. Excitation spectrum of RTA kinetic theory for imaginary wavenumbers. For the distribution function to be non-singular, [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Singular behavior of the candidate hydrodynamic distribution function [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
read the original abstract

By studying a simple model of relativistic particles propagating through a background medium with an energy-dependent relaxation time that is unbounded from above, we investigate how long-term memory obstructs the emergence of local hydrodynamics in systems with a gapless non-hydrodynamic sector. In the RTA matching frame, we show that the full gradient expansion is generically divergent in most flows, even for Fourier modes, and that any resummation necessarily retains an infinite set of slow non-hydrodynamic degrees of freedom. The divergence of the gradient expansion therefore reflects a more fundamental breakdown of hydrodynamic locality caused by persistent non-hydrodynamic memory. We finally show that sufficiently singular relaxation spectra can invalidate ordinary diffusion itself. In these regimes, the diffusivity diverges, and the late-time dynamics become superdiffusive, governed by intrinsically nonlocal constitutive relations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The paper studies a model of relativistic particles propagating through a background medium with an energy-dependent relaxation time unbounded from above. In the RTA matching frame, it shows that the full gradient expansion is generically divergent even for Fourier modes, that any resummation retains an infinite set of slow non-hydrodynamic modes, and that this signals a fundamental breakdown of hydrodynamic locality due to persistent memory. For sufficiently singular relaxation spectra the diffusivity diverges, ordinary diffusion fails, and late-time dynamics become superdiffusive and governed by intrinsically nonlocal constitutive relations.

Significance. If the model calculations are correct, the work supplies a concrete, falsifiable example in which a gapless non-hydrodynamic sector with singular spectrum prevents the emergence of local hydrodynamics and produces superdiffusion. This is useful for mapping the boundary between hydrodynamic and non-hydrodynamic regimes in relativistic kinetic theory and for motivating nonlocal constitutive relations. The result is model-specific and does not claim universality, which keeps the claim proportionate.

minor comments (3)
  1. The abstract states that the gradient expansion diverges 'even for Fourier modes' but does not indicate in which section the explicit mode-by-mode calculation or the radius-of-convergence argument appears; a forward reference would help readers locate the central technical result.
  2. The phrase 'RTA matching frame' is used without a one-sentence reminder of its definition or its relation to the standard relaxation-time approximation; adding this would improve accessibility for readers outside the immediate subfield.
  3. Figure captions (if present) should explicitly state whether the plotted quantities are obtained from the resummed series or from direct solution of the kinetic equation, to avoid ambiguity about what is being compared.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive and accurate summary of our work, as well as the recommendation for minor revision. No specific major comments are provided in the report.

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper analyzes a specific model of relativistic particles with energy-dependent relaxation time (unbounded above) in the RTA matching frame. All central claims—the divergence of the gradient expansion, retention of non-hydrodynamic modes, and emergence of superdiffusive nonlocal dynamics—are direct consequences of solving the model's kinetic equations under the stated assumptions. No step reduces by construction to a fitted parameter renamed as prediction, a self-definition, or a load-bearing self-citation chain. The results remain model-specific and falsifiable within the given framework, with no evidence of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the central setup rests on the choice of relaxation spectrum; no free parameters, axioms, or invented entities are explicitly quantified beyond the model definition.

axioms (1)
  • domain assumption The relaxation time is energy-dependent and unbounded from above.
    This is the key setup of the model studied in the RTA matching frame.

pith-pipeline@v0.9.1-grok · 5671 in / 1253 out tokens · 26696 ms · 2026-06-28T12:24:08.271385+00:00 · methodology

discussion (0)

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Reference graph

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