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arxiv: 2604.17392 · v1 · submitted 2026-04-19 · ✦ hep-ph · nucl-th

Recognition: unknown

Boost-invariant perfect Fermi-Dirac spin hydrodynamics

Zbigniew Drogosz , Natalia {\L}ygan
Authors on Pith no claims yet

Pith reviewed 2026-05-10 06:00 UTC · model grok-4.3

classification ✦ hep-ph nucl-th
keywords spin hydrodynamicsFermi-Dirac statisticsBoltzmann approximationboost-invariantspin polarization tensorperfect fluidheavy ion collisions
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The pith

Fermi-Dirac statistics produce hydrodynamic evolutions that differ from Boltzmann results by amounts smaller than spin feedback corrections in boost-invariant spin hydrodynamics.

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

This paper examines the impact of replacing the Boltzmann approximation with full Fermi-Dirac statistics in numerical models of perfect spin hydrodynamics for spin-1/2 particles. The setup maintains boost invariance and transverse homogeneity, with spin effects included to specified orders in the polarization tensor. It demonstrates that the resulting integral expressions for coefficients can be parametrized for practical computation. For initial conditions from earlier studies, the changes due to statistics are roughly ten times smaller than those induced by spin feedback. This indicates that the simpler Boltzmann treatment remains a good approximation in many cases while allowing checks on when quantum statistics matter.

Core claim

In boost-invariant transversely homogeneous perfect spin hydrodynamics with second-order corrections to the baryon current and energy-momentum tensor in the spin polarization tensor ω and first-order spin tensor, the evolution of parameters under Fermi-Dirac statistics differs from the Boltzmann case by amounts about one order of magnitude smaller than the corrections arising from spin feedback, and the numerical approach is feasible through parametrization of the special functions involved.

What carries the argument

The ordering of corrections in powers of the spin polarization tensor ω, combined with parametrization of Fermi-Dirac integral functions in the hydrodynamic coefficients, under boost-invariant transversely homogeneous flow.

If this is right

  • The numerical solutions can be obtained reliably for moderate values of spin polarization.
  • Breakdown of solutions occurs at very large spin polarization in one of the geometric configurations.
  • Spin feedback effects dominate the evolution over the choice of particle statistics.
  • Previous works using Boltzmann approximation capture the main features accurately for the considered initial conditions.

Where Pith is reading between the lines

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

  • This supports using Boltzmann statistics as a default in spin hydrodynamics simulations unless high precision on quantum effects is needed.
  • Extensions to non-boost-invariant or inhomogeneous geometries could reveal larger statistical differences.
  • Testing the breakdown condition experimentally in heavy-ion collisions might constrain the range of applicability of perfect spin hydrodynamics.

Load-bearing premise

The corrections to the baryon current and energy-momentum tensor can be treated as second order in the spin polarization while keeping the spin tensor first order, and the boost-invariant transversely homogeneous geometry holds during the entire evolution.

What would settle it

A direct numerical comparison showing that the evolution differences between Fermi-Dirac and Boltzmann statistics exceed the magnitude of spin feedback corrections for the initial conditions used in prior studies would falsify the main result.

Figures

Figures reproduced from arXiv: 2604.17392 by Natalia {\L}ygan, Zbigniew Drogosz.

Figure 1
Figure 1. Figure 1: Schematic view of the longitudinal and the transverse configuration [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Proper-time dependence of coefficients Ckz, Cωz of the spin polarization tensor in the longitudinal configuration in the Fermi–Dirac case (left column) and the relative differences between the Fermi–Dirac and the Boltzmann case, defined as δCkz ≡ CkzFD/CkzB − 1, δCωz ≡ CωzFD/CωzB − 1 (right column). The initial values of coefficients Ckz and Cωz are 0.25 (top row), 0.5 (middle row), or 0.75 (bottom row). 4… view at source ↗
Figure 3
Figure 3. Figure 3: Proper-time dependence of coefficients Ckx, Cωx, of the spin polarization tensor in the transverse configuration in the Fermi–Dirac case (left column) and the relative differences between the Fermi–Dirac and the Boltzmann case, δCkx ≡ CkxFD/CkxB − 1, δCωx ≡ CωxFD/CωxB − 1 (right column). The initial values of coefficients Ckx, Cky, Cωx, Cωy are 0.25 (top row), 0.5 (middle row), or 0.75 (bottom row). Owing … view at source ↗
read the original abstract

We analyze the effect of using the Fermi-Dirac statistics, rather than its Boltzmann approximation, in numerical simulations of perfect spin hydrodynamics of particles with spin 1/2. The system considered is boost invariant, transversely homogeneous, with corrections to the baryon current and the energy-momentum tensor that are second order in the spin polarization tensor $\omega$, and the spin tensor considered is first order in $\omega$. The study shows the feasibility of this approach, as the special functions defined by integrals that appear in the coefficients in the Fermi-Dirac case can be conveniently parametrized. For sets of initial conditions used in previous works, the differences in parameter evolution between the two underlying particle statistics are about one order of magnitude smaller than corrections coming from spin feedback. We also discuss when and why the numerical solutions of the equations of perfect spin hydrodynamics break down for very large values of spin polarization in one of the geometric configurations considered.

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

2 major / 1 minor

Summary. The paper analyzes the effect of Fermi-Dirac statistics versus the Boltzmann approximation in numerical simulations of perfect spin hydrodynamics for spin-1/2 particles. The setup is boost-invariant and transversely homogeneous, with baryon current and energy-momentum tensor corrections kept second-order in the spin polarization tensor ω while the spin tensor is first-order in ω. It demonstrates that the special functions in the Fermi-Dirac coefficients can be parametrized for numerical use, and reports that for initial conditions from prior works, the differences in parameter evolution between the statistics are about one order of magnitude smaller than spin-feedback corrections. The paper also discusses the conditions for numerical breakdown at very large spin polarization.

Significance. If the central claim holds, the result supports the practical sufficiency of the Boltzmann approximation in this class of spin-hydrodynamic simulations, since statistical differences are subdominant to spin effects. This could simplify modeling in applications such as heavy-ion collisions. The explicit parametrization of the Fermi-Dirac integrals is a concrete technical contribution that enables the reported numerics.

major comments (2)
  1. The central claim that Fermi-Dirac vs. Boltzmann differences are ~10× smaller than spin corrections for previous-work initial conditions rests on the maintained validity of the boost-invariant, transversely homogeneous ansatz and the strict second-order truncation in ω throughout the evolution. The manuscript notes numerical breakdown for large ω but does not provide explicit checks (e.g., time evolution of |ω| or higher-order residuals) confirming that the chosen initial conditions keep the system inside the regime where the ordering and geometry remain self-consistent; without this, the reported ordering of effects cannot be guaranteed inside the stated framework.
  2. The feasibility statement for the Fermi-Dirac case relies on parametrization of the special functions arising from the integrals. No quantitative error bounds, convergence tests against direct integration, or sensitivity analysis of the reported parameter differences to the parametrization accuracy are supplied; if the parametrization error is comparable to the ~10× smaller statistical difference, the comparison between statistics would be compromised.
minor comments (1)
  1. The abstract and introduction would benefit from a brief statement of the typical magnitude of ω (or range of initial conditions) for which the ordering is expected to hold, to make the domain of applicability clearer.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment point by point below and agree that the suggested additions will strengthen the presentation of our results.

read point-by-point responses

  1. Referee: The central claim that Fermi-Dirac vs. Boltzmann differences are ~10× smaller than spin corrections for previous-work initial conditions rests on the maintained validity of the boost-invariant, transversely homogeneous ansatz and the strict second-order truncation in ω throughout the evolution. The manuscript notes numerical breakdown for large ω but does not provide explicit checks (e.g., time evolution of |ω| or higher-order residuals) confirming that the chosen initial conditions keep the system inside the regime where the ordering and geometry remain self-consistent; without this, the reported ordering of effects cannot be guaranteed inside the stated framework.

    Authors: We agree that explicit verification of the regime of validity for the selected initial conditions is important to confirm self-consistency. In the revised manuscript we will add plots of the time evolution of |ω| for all initial conditions considered, together with estimates of the magnitude of higher-order terms in ω. These additions will demonstrate that the boost-invariant, transversely homogeneous ansatz and the second-order truncation remain valid throughout the evolution, thereby supporting the reported ordering of statistical versus spin-feedback effects. revision: yes

  2. Referee: The feasibility statement for the Fermi-Dirac case relies on parametrization of the special functions arising from the integrals. No quantitative error bounds, convergence tests against direct integration, or sensitivity analysis of the reported parameter differences to the parametrization accuracy are supplied; if the parametrization error is comparable to the ~10× smaller statistical difference, the comparison between statistics would be compromised.

    Authors: We acknowledge the need for quantitative validation of the parametrization. In the revised version we will include direct comparisons of the parametrized functions against numerical integration of the defining integrals, together with explicit error bounds and a sensitivity study showing the effect of parametrization inaccuracies on the reported differences between Fermi-Dirac and Boltzmann evolution. This will confirm that parametrization errors lie well below the scale of the statistical differences. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper performs numerical simulations of boost-invariant transversely homogeneous perfect spin hydrodynamics, parametrizing special functions arising in the Fermi-Dirac case to demonstrate feasibility. It then compares parameter evolution under Fermi-Dirac versus Boltzmann statistics for initial conditions drawn from prior literature, reporting that the observed differences are smaller than spin-feedback corrections. This comparison is an empirical outcome of integrating the stated hydrodynamic equations under fixed ordering (baryon current and EMT corrections second-order in ω, spin tensor first-order) and geometry; no step in the reported chain reduces by construction to a fitted parameter renamed as a prediction, a self-definitional relation, or a load-bearing self-citation that would force the result. The framework assumptions are explicitly declared and the breakdown for large ω is noted as a limitation, keeping the central claim self-contained as a numerical finding rather than a tautology.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central numerical comparison rests on the hydrodynamic equations being closed at the stated orders in ω and on the validity of the boost-invariant transversely homogeneous ansatz; no new particles or forces are introduced.

free parameters (1)
  • parametrization coefficients for Fermi-Dirac integrals
    The abstract states that the special functions are conveniently parametrized, implying fitted parameters chosen to match the integrals.
axioms (2)
  • domain assumption The system remains boost-invariant and transversely homogeneous throughout the evolution
    Stated in the abstract as the geometry considered.
  • domain assumption Corrections to baryon current and energy-momentum tensor are second order in ω while spin tensor is first order
    Explicitly stated as the truncation used in the study.

pith-pipeline@v0.9.0 · 5456 in / 1401 out tokens · 25113 ms · 2026-05-10T06:00:45.425260+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

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

  1. Boost-invariant and cylindrically symmetric perfect spin hydrodynamics

    hep-ph 2026-05 unverdicted novelty 5.0

    In boost-invariant cylindrical spin hydrodynamics, azimuthal-longitudinal coupling in the spin tensor produces nonzero total polarization only via the longitudinal magnetic component coupled to the azimuthal electric ...

Reference graph

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