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arxiv: 2512.08007 · v1 · pith:VHDI5JZQnew · submitted 2025-12-08 · ✦ hep-ph · nucl-th

(3+1)D event-by-event pre-equilibrium dynamics in heavy-ion collisions

Xiaojian Du , S\"oren Schlichting , Jie Zhu This is my paper

Pith reviewed 2026-05-22 12:30 UTC · model grok-4.3

classification ✦ hep-ph nucl-th
keywords heavy ion collisionspre-equilibrium dynamicsanisotropic flowlongitudinal structurekinetic theoryhydrodynamics3+1D simulations
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The pith

Extending pre-equilibrium dynamics to three dimensions plus time reveals sensitivity of longitudinal flow to hydrodynamic initialization time.

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

This work develops a three-dimensional framework for evolving initial conditions in heavy-ion collisions using response functions from kinetic theory that do not assume boost invariance. The full evolution from initial state through pre-equilibrium, hydrodynamics, and particle production is simulated to study how the start time of the hydrodynamic phase affects observables. Particular attention is paid to the longitudinal structure of anisotropic flow. A reader would care because early-time uncertainties limit what can be learned about the hot dense matter created in these collisions.

Core claim

The paper establishes that non-boost-invariant fluctuations can be propagated using three-plus-one-dimensional response functions derived from kinetic theory, and that this allows a complete simulation showing the dependence of the longitudinal structure of anisotropic flow on the time at which hydrodynamic evolution begins.

What carries the argument

The three-plus-one-dimensional response functions from kinetic theory that evolve the initial energy-momentum tensor while accounting for longitudinal fluctuations.

If this is right

  • Simulations can now capture the full space-time evolution without boost invariance assumptions.
  • Observables such as anisotropic flow vary with the choice of hydrodynamic start time.
  • The shear stress tensor approaches Navier-Stokes estimates as the system evolves toward equilibrium.
  • Event-by-event studies of pre-equilibrium effects become possible in full three dimensions.

Where Pith is reading between the lines

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

  • Matching these predictions to experimental data could constrain the duration of the pre-equilibrium phase.
  • This method might be combined with other initial state models to study a broader range of collision systems.
  • Variations in flow structures could provide new tests of hydrodynamic descriptions at early times.

Load-bearing premise

The kinetic theory response functions accurately capture the evolution of fluctuations until the system reaches the hydrodynamic regime.

What would settle it

Experimental data on the rapidity dependence of anisotropic flow that does not match the predicted changes when varying the hydrodynamic initialization time would challenge the results.

Figures

Figures reproduced from arXiv: 2512.08007 by Jie Zhu, S\"oren Schlichting, Xiaojian Du.

Figure 1
Figure 1. Figure 1: Evolution of the energy response (Gs s (∣kT∣∆τ, kη)) and longitudinal momentum response (Gs,η s (∣kT∣∆τ, kη)) to an initial energy perturbation as a function of ∣kT∣∆τ and kη. Different panels correspond to different points in time. The color indicates the magnitude of respective response functions. 0.0 0.5 1.0 1.5 |r|/( 0) 2 0 2 1 0 1 0.01 ( 0) 2 G s s (|r|/( 0), , ) 0.0 0.5 1.0 1.5 |r|/( 0) 2 0 2 1 0 1 0… view at source ↗
Figure 2
Figure 2. Figure 2: Evolution of the energy response (Gs s (∣r∣/∆τ, η)) and longitudinal momentum response (Gs,η s (∣r∣/∆τ, η)) to an initial energy perturbation as a function of ∣r∣/∆τ and η. Different panels correspond to different points in time. The color indicates the magnitude of respective response functions [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Examination of the constitutive relations, Eqs.(21) and (22), at scaled times [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of the energy response functions in QCD and in RTA for [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Time evolution of the energy density τe(x, y, ηs) during the kinetic-theory pre-equilibrium stage, shown as two-dimensional cuts in the transverse plane at ηs = 0 (top) and in the reaction plane at y = 0 fm (bottom). B. Hydrodynamic fields Next, to examine the transition from the kinetic pre￾equilibrium stage to hydrodynamics, we first consider the transversely averaged hydrodynamic fields, namely the ener… view at source ↗
Figure 5
Figure 5. Figure 5: Three-dimensional energy density distribution [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Transverse average of τe3/4 , transverse velocity v⊥ and momentum eccentricity as a function of time τ in midrapidity (ηs=0) and forward rapidity (ηs = 5). The three average fields are plotted for different hydrodynamic initialization time τhydro. tiny differences originating from the switch from a con￾formal equation of state to a realistic QCD equation of state [71, 72]. On the other hand, we find that t… view at source ↗
Figure 8
Figure 8. Figure 8: Local profile of energy density τe3/4 and flow velocity vx (or vηs ) for different hydrodynamics transition times τhydro in transverse plane (left panels) or longitudinal direction (right panels). dynamic stage, we expect that, for reasonable values, the choice of the matching time τhydro does not significantly affect the final state hadronic observables. We first demonstrate the effects of hydrodynamiza￾t… view at source ↗
Figure 9
Figure 9. Figure 9: Comparison of the out-of-equilibrium shear stress tensor with the Navier-Stokes estimate at different [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Scaled evolution time variable ω˜Id at different hydro starting times. Values of ω˜Id > 1 indicate that the system is close enough to local thermal equilibrium for hydrodynamics to become applicable [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Dependence of charged particle multiplicity [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: Sensitivity of the pT and η dependence of anisotropic flow v2, v3 to hydro starting time τhydro. propagation of information from initial conditions. Al￾though these aspects are conceptually straightforward, they are computationally expensive. We also aim to ex￾plore the applicability of the KøMPøST framework by pushing the simulations to smaller system sizes and lower collision energies, where the duratio… view at source ↗
Figure 14
Figure 14. Figure 14: Evolution of the background energy density [PITH_FULL_IMAGE:figures/full_fig_p019_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Evolution of transverse momentum response ( [PITH_FULL_IMAGE:figures/full_fig_p021_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Evolution of the transverse momentum response ( [PITH_FULL_IMAGE:figures/full_fig_p022_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Hydrodynamization of more components of shear stress tensor [PITH_FULL_IMAGE:figures/full_fig_p023_17.png] view at source ↗
read the original abstract

So far a major source of uncertainty in the study of heavy-ion collisions arises from the early time dynamics which includes initial state and pre-equilibrium dynamics. The state-of-the-art framework, KoMPoST, employs non-equilibrium Green's functions to propagate the initial energy-momentum tensor to the hydrodynamic phase, yet currently only treats transverse plane dynamics under boost-invariant conditions. In this work, we extend KoMPoST to include non-boost-invariant responses to initial conditions, essential for accurately capturing the longitudinal structures observed in heavy-ion collisions. Non-boost-invariant fluctuations on top of a homogeneous background are evolved using (3+1)D response functions calculated in kinetic theory. To assess kinetic theory's transition towards hydrodynamic evolution, we systematically compare the out-of-equilibrium shear-stress tensor from KoMPoST-3D with estimates based on Navier-Stokes hydrodynamics. Subsequently, a comprehensive (3+1)D framework, McDIPPER+KoMPoST-3D+CLVisc+SMASH, is utilized to simulate the complete spacetime evolution of heavy-ion collisions. The sensitivity of key observables, including longitudinal structure of anisotropic flow, to variations in the hydrodynamic initialization time is thoroughly investigated.

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 / 2 minor

Summary. The paper extends the KoMPoST framework from boost-invariant transverse dynamics to (3+1)D non-boost-invariant pre-equilibrium evolution. It computes kinetic-theory response functions for non-boost-invariant fluctuations superimposed on a homogeneous background, compares the resulting out-of-equilibrium shear-stress tensor to Navier-Stokes estimates, and then deploys the full event-by-event chain McDIPPER + KoMPoST-3D + CLVisc + SMASH to study the sensitivity of longitudinal structures in anisotropic flow (and other observables) to the hydrodynamic initialization time.

Significance. If the linear-response superposition remains accurate for realistic McDIPPER fluctuation amplitudes, the work supplies a practical route to incorporate longitudinal pre-equilibrium dynamics into full (3+1)D heavy-ion simulations, directly addressing a major source of uncertainty in early-time modeling. The systematic NS comparison and the complete simulation pipeline are concrete strengths that would be valuable to the community.

major comments (2)
  1. [Abstract (description of KoMPoST-3D extension) and the section detailing the response-function construction] The central claim that the framework captures the sensitivity of longitudinal flow structure to initialization time rests on the assumption that (3+1)D response functions computed on a homogeneous background can be linearly superposed to evolve the full fluctuating T^{μν} from McDIPPER. No direct validation against nonlinear kinetic evolution on inhomogeneous backgrounds with realistic transverse gradients is described; if the response deviates for the fluctuation amplitudes present in McDIPPER, both the pre-equilibrium evolution and the reported sensitivities would be affected.
  2. [Section on comparison of out-of-equilibrium shear-stress tensor] The abstract states that the shear-stress tensor from KoMPoST-3D is compared only to Navier-Stokes estimates. A quantitative assessment (e.g., relative difference as a function of proper time or fluctuation amplitude) is needed to establish how far the kinetic-theory result departs from hydrodynamics before the switch time; without such metrics the transition assessment remains qualitative.
minor comments (2)
  1. [Methodology section] Notation for the (3+1)D response functions and the decomposition into background plus fluctuation should be defined explicitly with an equation number for later reference.
  2. [Results figures] Figure captions should include the specific initialization times varied and the collision system (e.g., Pb-Pb at 5.02 TeV) to allow immediate interpretation of the sensitivity plots.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation of our work and for the constructive comments. We address each major comment below and indicate the revisions made to the manuscript.

read point-by-point responses

  1. Referee: The central claim that the framework captures the sensitivity of longitudinal flow structure to initialization time rests on the assumption that (3+1)D response functions computed on a homogeneous background can be linearly superposed to evolve the full fluctuating T^{μν} from McDIPPER. No direct validation against nonlinear kinetic evolution on inhomogeneous backgrounds with realistic transverse gradients is described; if the response deviates for the fluctuation amplitudes present in McDIPPER, both the pre-equilibrium evolution and the reported sensitivities would be affected.

    Authors: We acknowledge that a direct numerical validation of the linear superposition against full nonlinear kinetic evolution on inhomogeneous backgrounds would strengthen the central claim. Such a validation is computationally demanding and was not performed in the present study. The approach extends the established linear-response framework of the original (2+1)D KoMPoST, where comparable approximations have been used successfully. In the revised manuscript we have added an explicit discussion of the expected range of validity, referencing the typical fluctuation amplitudes extracted from McDIPPER and noting that nonlinear corrections remain a topic for future work. revision: partial

  2. Referee: The abstract states that the shear-stress tensor from KoMPoST-3D is compared only to Navier-Stokes estimates. A quantitative assessment (e.g., relative difference as a function of proper time or fluctuation amplitude) is needed to establish how far the kinetic-theory result departs from hydrodynamics before the switch time; without such metrics the transition assessment remains qualitative.

    Authors: We agree that quantitative metrics improve the clarity of the comparison. In the revised manuscript we have added plots and tables showing the relative difference between the KoMPoST-3D shear-stress tensor and the Navier-Stokes estimate as a function of proper time, for several representative fluctuation amplitudes. These additions make the assessment of the hydrodynamic transition quantitative rather than qualitative. revision: yes

Circularity Check

0 steps flagged

No significant circularity; independent (3+1)D kinetic response functions and full-event simulations

full rationale

The paper computes new (3+1)D response functions in kinetic theory for non-boost-invariant fluctuations on a homogeneous background, then superposes them onto McDIPPER initial conditions before switching to hydrodynamics. This calculation is performed independently and compared against Navier-Stokes estimates as an external benchmark. The subsequent sensitivity study of longitudinal flow structure to initialization time is obtained from complete McDIPPER+KoMPoST-3D+CLVisc+SMASH event simulations; none of these steps reduce by definition or by self-citation to quantities already fitted inside the present work. Prior KoMPoST references provide context but are not load-bearing for the new 3D extension or the reported sensitivities.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The framework rests on the validity of kinetic-theory response functions for longitudinal fluctuations and on the choice of hydrodynamic initialization time as a tunable parameter whose effect is studied.

free parameters (1)
  • hydrodynamic initialization time
    Varied systematically to assess sensitivity of longitudinal flow observables.
axioms (1)
  • domain assumption Kinetic theory response functions accurately capture non-boost-invariant pre-equilibrium evolution until hydrodynamics applies
    Invoked to evolve (3+1)D fluctuations on a homogeneous background.

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Forward citations

Cited by 1 Pith paper

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Reference graph

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