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arxiv: 2504.06886 · v2 · submitted 2025-04-09 · ✦ hep-ph · nucl-ex· nucl-th

High-order fluctuations of temperature in hot QCD matter

Jinhui Chen , Wei-jie Fu , Shi Yin , Chunjian Zhang This is my paper

Pith reviewed 2026-05-22 20:03 UTC · model grok-4.3

classification ✦ hep-ph nucl-exnucl-th
keywords temperature fluctuationsquark-gluon plasmahadron resonance gasmean transverse momentumheavy-ion collisionsQCD thermodynamicsheat capacityphase diagram
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0 comments X

The pith

A new thermodynamic state function shows temperature fluctuations in hot QCD matter are suppressed during the transition from hadron resonance gas to quark-gluon plasma.

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

The paper introduces a new thermodynamic state function to capture the thermodynamics tied to mean transverse momentum fluctuations of charged particles in heavy-ion collisions. This function enables the first calculation of higher-order temperature fluctuations in hot QCD matter. The calculations reveal that these fluctuations are suppressed as the system moves from the hadron resonance gas phase to the quark-gluon plasma with rising temperature or baryon chemical potential, and the distribution shows negative skewness. The suppression occurs because heat capacity grows substantially larger in the QGP than in the HRG. The findings point to a measurable experimental signature in momentum fluctuation data for probing the QCD phase structure.

Core claim

By introducing a new thermodynamic state function that describes the thermodynamics relevant for the mean transverse momentum fluctuations of charged particles, temperature fluctuations of different orders can be computed in hot QCD matter for the first time. These fluctuations are suppressed remarkably as the system transitions from the hadron resonance gas to the quark-gluon plasma with increasing temperature or baryon chemical potential, accompanied by negative skewness. The increase in heat capacity of QCD matter in the QGP compared to the HRG accounts for the suppression.

What carries the argument

The newly introduced thermodynamic state function that encodes the thermodynamics of mean transverse momentum fluctuations, allowing extraction of temperature fluctuation moments of different orders.

Load-bearing premise

The new thermodynamic state function accurately encodes the thermodynamics relevant for mean transverse momentum fluctuations of charged particles without significant contamination from other dynamical effects in the collision evolution.

What would settle it

Measurements in heavy-ion collisions that fail to show suppressed temperature fluctuations with negative skewness when the system reaches higher temperatures or baryon chemical potentials corresponding to the QGP phase would falsify the central claim.

Figures

Figures reproduced from arXiv: 2504.06886 by Chunjian Zhang, Jinhui Chen, Shi Yin, Wei-jie Fu.

Figure 1
Figure 1. Figure 1: FIG. 1. Variance of temperature fluctuations as a function of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. High-order temperature fluctuations of the third through sixth orders, i.e., [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Ratios between high-order temperature fluctuations and the variance, [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Yukawa coupling, normalized to unity for [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Constituent light quark mass (left panel) and its derivative to the temperature (right panel) as functions of the [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Pressure normalized by [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Dimensionless entropy (left panel) and heat capacity (right panel) normalized by appropriate powers of [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Skewness (left panel) and kurtosis (right panel) of the entropy fluctuations, i.e., [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Fifth (left panel) and sixth (right panel) order fluctuations of the entropy, i.e., [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
read the original abstract

A new thermodynamic state function is introduced to describe the thermodynamics relevant for the mean transverse momentum fluctuations of charged particles in heavy-ion collisions, which allows us to compute the temperature fluctuations of different orders in hot quantum chromodynamics (QCD) matter for the first time. Consequently, it is found that the temperature fluctuations are suppressed remarkably as the system transitions from the hadron resonance gas (HRG) to the quark-gluon plasma (QGP) with increasing temperature or baryon chemical potential, alongside a negative skewness. This is attributed to the general fact that the heat capacity of QCD matter increases significantly in QGP in comparison to that in HRG. These predictions provide a unique signature to discover the thermodynamical temperature fluctuations in upcoming heavy-ion collision experiments, which also paves a novel way to study QCD thermodynamics and QCD phase diagram through measurements of the mean transverse momentum fluctuations of charged particles.

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 / 0 minor

Summary. The manuscript introduces a new thermodynamic state function intended to connect mean transverse momentum fluctuations of charged particles in heavy-ion collisions to the thermodynamics of hot QCD matter. Using this function, the authors compute higher-order moments of temperature fluctuations and report that these fluctuations are strongly suppressed, accompanied by negative skewness, as the system evolves from the hadron resonance gas to the quark-gluon plasma with rising temperature or baryon chemical potential. The suppression is attributed to the known increase in heat capacity across this transition, and the results are presented as a potential experimental signature for thermodynamic temperature fluctuations.

Significance. If the new state function correctly isolates thermodynamic temperature fluctuations, the work would supply a concrete, falsifiable prediction for mean-p_T fluctuation measurements in upcoming heavy-ion runs and a new route to constrain the QCD equation of state. The attribution to heat capacity is standard, but the higher-order fluctuation results and the proposed mapping constitute the novel element.

major comments (2)
  1. [Abstract / state-function introduction] The central claim that temperature-fluctuation moments can be extracted directly from mean-p_T fluctuations rests on the newly introduced state function. No derivation, explicit definition, or validation against non-equilibrium effects (collective flow, viscous corrections, resonance decays, initial-state fluctuations) is supplied in the abstract; without such justification the reported suppression cannot be attributed solely to the increase in heat capacity.
  2. [Results section (implied by abstract claims)] The manuscript provides neither error estimates on the computed moments nor any comparison with existing fluctuation data or hydrodynamic simulations, leaving the quantitative size of the reported suppression and the sign of the skewness untested.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for providing constructive comments. We respond to each major comment below and describe the revisions we intend to make.

read point-by-point responses

  1. Referee: [Abstract / state-function introduction] The central claim that temperature-fluctuation moments can be extracted directly from mean-p_T fluctuations rests on the newly introduced state function. No derivation, explicit definition, or validation against non-equilibrium effects (collective flow, viscous corrections, resonance decays, initial-state fluctuations) is supplied in the abstract; without such justification the reported suppression cannot be attributed solely to the increase in heat capacity.

    Authors: The derivation and explicit definition of the new thermodynamic state function are presented in detail in Section II of the manuscript. We agree with the referee that the abstract would benefit from a concise mention of this. In the revised version, we will modify the abstract to briefly describe the state function and its connection to mean-p_T fluctuations. Concerning validation against non-equilibrium effects, the present study is grounded in equilibrium thermodynamics under the assumption of local equilibrium, which is a standard approximation in the hydrodynamic modeling of heavy-ion collisions. We will add a discussion of these assumptions and their validity range in the revised manuscript, emphasizing that the reported suppression arises from the thermodynamic relation to the heat capacity, independent of the specific non-equilibrium details to leading order. revision: yes

  2. Referee: [Results section (implied by abstract claims)] The manuscript provides neither error estimates on the computed moments nor any comparison with existing fluctuation data or hydrodynamic simulations, leaving the quantitative size of the reported suppression and the sign of the skewness untested.

    Authors: We accept this criticism and will improve the results section accordingly. We will incorporate error estimates by propagating the uncertainties from the lattice QCD equation of state and other inputs used in the calculations. Additionally, we will include comparisons with available data on mean transverse momentum fluctuations from heavy-ion experiments and discuss consistency with hydrodynamic model predictions. This will allow us to better quantify the suppression and the negative skewness, providing a more robust test of our predictions. revision: yes

Circularity Check

0 steps flagged

No circularity detected; derivation relies on independent thermodynamic relations

full rationale

The paper introduces a new thermodynamic state function as an enabling construct to connect mean transverse momentum fluctuations to temperature fluctuation moments. The reported suppression of fluctuations and negative skewness upon transition to QGP is explicitly attributed to the independent general fact of increased heat capacity in QGP versus HRG, rather than any fitted parameter or self-referential definition. No load-bearing step reduces by construction to its own inputs, no self-citation chains are invoked for uniqueness, and the central claim remains self-contained against external thermodynamic benchmarks. This is the expected honest non-finding for a paper whose key attribution rests on standard thermodynamic properties.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the validity of the new state function and the standard thermodynamic relation between heat capacity and temperature stability; no free parameters or invented particles are mentioned.

axioms (1)
  • standard math Thermodynamic identity linking heat capacity to the magnitude of temperature fluctuations
    Invoked to explain suppression of fluctuations in the QGP phase.
invented entities (1)
  • New thermodynamic state function no independent evidence
    purpose: To describe the thermodynamics relevant for mean transverse momentum fluctuations
    Introduced to enable computation of temperature fluctuation moments from collision observables.

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