pith. sign in

arxiv: 2606.02446 · v1 · pith:HNGJJNH6new · submitted 2026-06-01 · ✦ hep-th · cond-mat.stat-mech· hep-ph· nucl-th

Cumulant dynamics in finite-memory diffusion

Navid Abbasi , Xin An , Shanjin Wu This is my paper

Pith reviewed 2026-06-28 13:30 UTC · model grok-4.3

classification ✦ hep-th cond-mat.stat-mechhep-phnucl-th
keywords cumulant dynamicsfinite-memory diffusionMaxwell-Cattaneo diffusionQCD critical pointquark-gluon plasmaconserved charge fluctuationsWigner functionsnon-monotonic behavior
0
0 comments X

The pith

Finite current memory suppresses and reshapes non-monotonic cumulant behavior in diffusion models of the 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 develops a dynamical description for how fluctuations of conserved charges evolve in the quark-gluon plasma using Maxwell-Cattaneo diffusion instead of the standard Fickian model. In this extended model the diffusive current relaxes over a finite time and therefore carries memory of past states. This memory adds an effect on top of the usual lag behind equilibrium values, leading to changes in how cumulants behave as the system evolves along trajectories in the phase diagram. A sympathetic reader would care because these cumulants are proposed signatures of the QCD critical point, so accurate modeling affects how experimental data from heavy-ion collisions are interpreted. The strongest effects appear in higher-order cumulants and their ratios.

Core claim

The central claim is that extending the diffusive evolution to include finite current relaxation time, via closed equations for multi-point Wigner functions, produces an additional memory effect that can suppress, shift, and reshape the non-monotonic behavior of acceptance-dependent cumulants relative to both instantaneous equilibrium and Fickian diffusion, with the most visible effects in higher-order cumulants and ratios along representative QCD phase diagram trajectories.

What carries the argument

Maxwell-Cattaneo diffusion, where the current relaxes on a finite time scale retaining memory, enabling derivation of closed evolution equations for multi-point Wigner functions.

If this is right

  • Cumulants lag behind their instantaneous equilibrium values due to ordinary diffusion.
  • Finite current relaxation adds a distinct memory-induced deviation on top of that lag.
  • Non-monotonic features in the cumulants become suppressed, shifted, or reshaped.
  • Higher-order cumulants and their ratios exhibit the largest sensitivity to the memory.
  • The resulting freezeout values depend on the specific trajectory taken through the phase diagram.

Where Pith is reading between the lines

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

  • Similar finite-memory corrections could matter in other transport settings where relaxation timescales overlap with system lifetimes.
  • Heavy-ion collision analyses searching for the critical point may need to include this baseline to avoid misinterpreting fluctuation data.
  • Varying the relaxation time parameter in simulations could identify regimes where memory effects dominate observable cumulant ratios.

Load-bearing premise

The current-relaxation time must be comparable to the relaxation time of the relevant fluctuation modes for the delayed-response effects to be non-negligible.

What would settle it

A direct comparison showing that measured cumulant ratios in heavy-ion collisions match Fickian diffusion predictions exactly, without additional suppression or shifting attributable to finite memory, would falsify the necessity of the Maxwell-Cattaneo extension.

Figures

Figures reproduced from arXiv: 2606.02446 by Navid Abbasi, Shanjin Wu, Xin An.

Figure 1
Figure 1. Figure 1: The mid-rapidity window in the longitudinal direction [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Schematic illustration of the background trajectories used in this work in the ( [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Time-dependent thermodynamic and transport inputs along the background evolution at [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Time evolution of the normalized two-point Wigner function [PITH_FULL_IMAGE:figures/full_fig_p021_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p022_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Time evolution of the normalized higher connected correlators along the far-from [PITH_FULL_IMAGE:figures/full_fig_p023_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p024_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The Wigner functions Wk=2,3,4(q, tf ) as function of q at freezeout time tf . The solid and dashed curves correspond to evolution trajectories at fixed µfar = 0.100 GeV and µnear = 0.366 GeV, respectively. The black curves represent the equilibrium values W eq k for µfar and µnear. The colored curves show the values of Wk(q, tf ) at different τ , including the Fickian limit when τ = 0 (blue curves). The ma… view at source ↗
Figure 9
Figure 9. Figure 9: Freezeout acceptance-dependent cumulants [PITH_FULL_IMAGE:figures/full_fig_p027_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Freezeout ratio observables Sσ ≡ C3/C2 and κσ2 ≡ C4/C2 at fixed acceptance width ∆y = 0.5, shown as functions of µ. Color conventions are the same as in [PITH_FULL_IMAGE:figures/full_fig_p028_10.png] view at source ↗
read the original abstract

Fluctuations of conserved charges are among the main proposed signatures of the quantum chromodynamics (QCD) critical point, but their interpretation requires a dynamical description of how fluctuation correlators evolve during the finite lifetime of the quark--gluon plasma (QGP) fireball. The standard baseline for this evolution is Fickian diffusion, in which the diffusive current follows the local density gradient instantaneously. This instantaneous-current limit can miss delayed-response effects when the current-relaxation time becomes comparable to the relaxation time of the relevant fluctuation modes. In this work we extend this baseline to Maxwell--Cattaneo diffusion, where the current relaxes on a finite time scale and therefore retains memory. We derive closed evolution equations for multi-point Wigner functions and convert the freezeout correlators into acceptance-dependent cumulants along representative trajectories in the QCD phase diagram. While Fickian diffusion already causes the correlators to lag behind their instantaneous equilibrium values, finite current relaxation introduces an additional memory effect beyond this diffusive lag. As a result, current memory can suppress, shift, and reshape the non-monotonic behavior of the cumulants relative to both instantaneous equilibrium and Fickian diffusion, with the most visible effects appearing in higher-order cumulants and their ratios.

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 paper extends the standard Fickian diffusion model for conserved-charge fluctuations in the QGP to Maxwell-Cattaneo diffusion with finite current-relaxation time. It derives closed evolution equations for multi-point Wigner functions, converts the resulting freezeout correlators into acceptance-dependent cumulants along representative QCD trajectories, and reports that finite memory suppresses, shifts, and reshapes the non-monotonic cumulant behavior relative to both instantaneous equilibrium and Fickian diffusion, with the strongest impact on higher-order cumulants and ratios.

Significance. If the central results hold, the work supplies a technically useful extension of dynamical fluctuation modeling for QCD critical-point searches. The derivation of closed multi-point Wigner-function equations constitutes a clear methodological advance over the instantaneous-current baseline.

major comments (2)
  1. [Abstract] Abstract: the claim that finite current memory produces observable reshaping beyond Fickian lag is conditioned on the current-relaxation time becoming comparable to the relaxation times of the relevant fluctuation modes. The manuscript does not verify that this timescale condition is satisfied for the representative trajectories or parameter choices used in the cumulant computations; without such verification the reported additional memory effects remain conditional.
  2. [Numerical results / freezeout conversion] Conversion procedure (freezeout to acceptance-dependent cumulants): the load-bearing step that maps the evolved multi-point Wigner functions to the final cumulants inherits the unverified timescale assumption; if the chosen relaxation time remains much smaller than the diffusive timescales set by system size or wave-number, the reshaping effect does not materialize and the comparison to Fickian diffusion collapses to the already-known lag.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our work. We address the two major comments point by point below, clarifying the parameter choices and proposing explicit additions to strengthen the presentation.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that finite current memory produces observable reshaping beyond Fickian lag is conditioned on the current-relaxation time becoming comparable to the relaxation times of the relevant fluctuation modes. The manuscript does not verify that this timescale condition is satisfied for the representative trajectories or parameter choices used in the cumulant computations; without such verification the reported additional memory effects remain conditional.

    Authors: We agree that observable reshaping beyond the Fickian lag requires the current-relaxation time to be comparable to the relaxation times of the relevant fluctuation modes. The representative trajectories and parameter sets in the manuscript were selected precisely so that this condition holds, which is why the computations exhibit suppression, shifts, and reshaping of the cumulants that are absent in the pure Fickian case. To remove any ambiguity we will add an explicit verification subsection (or appendix) that compares the current-relaxation time against the diffusive relaxation times set by system size and wave-number for each trajectory shown. revision: yes

  2. Referee: [Numerical results / freezeout conversion] Conversion procedure (freezeout to acceptance-dependent cumulants): the load-bearing step that maps the evolved multi-point Wigner functions to the final cumulants inherits the unverified timescale assumption; if the chosen relaxation time remains much smaller than the diffusive timescales set by system size or wave-number, the reshaping effect does not materialize and the comparison to Fickian diffusion collapses to the already-known lag.

    Authors: The conversion is performed on Wigner functions that have already evolved under the finite-memory dynamics. Because the reported cumulants display additional memory-induced features (suppression, shift, and reshaping) that are quantitatively distinct from the Fickian results, the timescale condition is satisfied for the displayed cases. Nevertheless, we accept that an explicit check would make the argument self-contained; we will therefore insert a short paragraph and accompanying table in the freezeout-conversion section that tabulates the relevant timescales for each trajectory and acceptance window. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation uses independent input scales

full rationale

The paper treats the current-relaxation time as an independent external scale that must be comparable to fluctuation-mode times for the reported memory effects to appear. Closed equations for multi-point Wigner functions are derived from the Maxwell-Cattaneo constitutive relation and then converted to acceptance-dependent cumulants along trajectories; neither step reduces a claimed prediction to a quantity defined in terms of a fitted parameter or to a self-citation chain. The abstract and derivation explicitly flag the timescale condition as an input assumption rather than an output, and no self-definitional, fitted-input-called-prediction, or ansatz-smuggled patterns are exhibited. The central claim therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the applicability of the Maxwell-Cattaneo constitutive relation to the QGP and on the existence of a relaxation time scale comparable to fluctuation mode times; no new particles or forces are postulated.

free parameters (1)
  • current relaxation time
    Finite time scale introduced in the Maxwell-Cattaneo model; its magnitude relative to fluctuation relaxation times controls the size of the reported memory effects.
axioms (2)
  • standard math Charge conservation
    Underlying the continuity equation that couples to the diffusive current.
  • domain assumption Validity of Maxwell-Cattaneo constitutive relation for QGP
    The extension assumes this hyperbolic diffusion model captures delayed response when relaxation times are comparable.

pith-pipeline@v0.9.1-grok · 5754 in / 1359 out tokens · 31603 ms · 2026-06-28T13:30:16.383551+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

83 extracted references · 68 canonical work pages · 28 internal anchors

  1. [1]

    Landau and E

    L. Landau and E. Lifshitz,Fluid Mechanics, vol. 6 ofCourse of Theoretical Physics, Elsevier Science (2013)

    2013

  2. [2]

    New theories of relativistic hydrodynamics in the LHC era

    W. Florkowski, M.P. Heller and M. Spalinski,New theories of relativistic hydrodynamics in the LHC era,Rept. Prog. Phys.81(2018) 046001 [1707.02282]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  3. [3]

    Fourier,Th´ eorie analytique de la chaleur, Firmin Didot, p` ere et fils (1822)

    J.-B.J. Fourier,Th´ eorie analytique de la chaleur, Firmin Didot, p` ere et fils (1822)

  4. [4]

    Fick,On liquid diffusion,The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science10(1855) 30

    A. Fick,On liquid diffusion,The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science10(1855) 30

  5. [5]

    Cattaneo,Sur une forme de l’´ equation de la chaleur ´ eliminant le paradoxe d’une propagation instantan´ ee,Comptes Rendus de l’Acad´ emie des Sciences247(1958) 431

    C. Cattaneo,Sur une forme de l’´ equation de la chaleur ´ eliminant le paradoxe d’une propagation instantan´ ee,Comptes Rendus de l’Acad´ emie des Sciences247(1958) 431

    1958

  6. [6]

    Vernotte,Les paradoxes de la th´ eorie continue de l’´ equation de la chaleur,Comptes Rendus de l’Acad´ emie des Sciences246(1958) 3154

    P. Vernotte,Les paradoxes de la th´ eorie continue de l’´ equation de la chaleur,Comptes Rendus de l’Acad´ emie des Sciences246(1958) 3154

    1958

  7. [7]

    Israel and J.M

    W. Israel and J.M. Stewart,Transient relativistic thermodynamics and kinetic theory,Annals Phys.118(1979) 341

    1979

  8. [8]

    Heller, A

    M.P. Heller, A. Serantes, M. Spali´ nski, V. Svensson and B. Withers,Transseries for causal diffusive systems,JHEP04(2021) 192 [2011.13864]

    work page arXiv 2021

  9. [9]

    Abbasi, M

    N. Abbasi, M. Kaminski and O. Tavakol,Theory of Nonlinear Diffusion with a Physical Gapped Mode,Phys. Rev. Lett.132(2024) 131602 [2212.11499]

    work page arXiv 2024

  10. [10]

    Abbasi, M

    N. Abbasi, M. Kaminski and D.H. Rischke,Comparison between causal and acausal diffusion: a Schwinger-Keldysh effective field theory perspective,JHEP03(2026) 156 [2506.20500]

    work page arXiv 2026

  11. [11]

    Causal UV completions of relativistic hydrodynamics

    R. Brants,Causal UV completions of relativistic hydrodynamics,2605.21377. 44

    work page internal anchor Pith review Pith/arXiv arXiv

  12. [12]

    Denicol and J

    G.S. Denicol and J. Noronha,Stochastic fluctuations and the relaxation time in transient relativistic fluids,Phys. Lett. B868(2025) 139773 [2406.15569]

    work page arXiv 2025

  13. [13]

    X. An, R. Brants, M.P. Heller and Y. Yin,Building far-from-equilibrium effective field theories using shift symmetries,arXiv:2511.11555 [hep-th]

    work page arXiv

  14. [14]

    Heaviside,On the extra current,Philosophical Magazine Series 52(1876) 135

    O. Heaviside,On the extra current,Philosophical Magazine Series 52(1876) 135

  15. [15]

    Brown, D

    P.T. Brown, D. Mitra, E. Guardado-Sanchez, R. Nourafkan, A. Reymbaut, C.-D. H´ ebert et al.,Bad metallic transport in a cold atom fermi-hubbard system,Science363(2019) 379

    2019

  16. [16]

    Chester,Second sound in solids,Phys

    M. Chester,Second sound in solids,Phys. Rev.131(1963) 2013

    1963

  17. [17]

    Hydro+: hydrodynamics with parametric slowing down and fluctuations near the critical point

    M. Stephanov and Y. Yin,Hydrodynamics with parametric slowing down and fluctuations near the critical point,Phys. Rev. D98(2018) 036006 [1712.10305]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  18. [18]

    X. An, G. Ba¸ sar, M. Stephanov and H.-U. Yee,Fluctuation dynamics in a relativistic fluid with a critical point,Phys. Rev. C102(2020) 034901 [1912.13456]

    work page arXiv 2020

  19. [19]

    Hydrodynamic Fluctuations, Long-time Tails, and Supersymmetry

    P. Kovtun and L.G. Yaffe,Hydrodynamic fluctuations, long time tails, and supersymmetry, Phys. Rev. D68(2003) 025007 [hep-th/0303010]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  20. [20]

    Roth and L

    J.V. Roth and L. von Smekal,Critical dynamics in a real-time formulation of the functional renormalization group,JHEP10(2023) 065 [2303.11817]

    work page arXiv 2023

  21. [21]

    Non-Gaussian fluctuations near the QCD critical point

    M.A. Stephanov,Non-Gaussian fluctuations near the QCD critical point,Phys. Rev. Lett. 102(2009) 032301 [0809.3450]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  22. [22]

    Third moments of conserved charges as probes of QCD phase structure

    M. Asakawa, S. Ejiri and M. Kitazawa,Third moments of conserved charges as probes of QCD phase structure,Phys. Rev. Lett.103(2009) 262301 [0904.2089]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  23. [23]

    X. An, F. Giglio and G. Landolfi,Phase transitions and finite-size effects in integrable virial statistical models,Phys. Rev. E113(2026) L042103 [2503.15719]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  24. [24]

    Search for the QCD Critical Point with Fluctuations of Conserved Quantities in Relativistic Heavy-Ion Collisions at RHIC : An Overview

    X. Luo and N. Xu,Search for the QCD Critical Point with Fluctuations of Conserved Quantities in Relativistic Heavy-Ion Collisions at RHIC : An Overview,Nucl. Sci. Tech.28 (2017) 112 [1701.02105]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  25. [25]

    Hadronic Fluctuations and Correlations

    V. Koch,Hadronic Fluctuations and Correlations, inRelativistic Heavy Ion Physics, R. Stock, ed., pp. 626–652, Springer-Verlag Berlin Heidelberg (2010), DOI [0810.2520]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  26. [26]

    Fluctuations of conserved charges in relativistic heavy ion collisions: An introduction

    M. Asakawa and M. Kitazawa,Fluctuations of conserved charges in relativistic heavy ion collisions: An introduction,Prog. Part. Nucl. Phys.90(2016) 299 [1512.05038]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  27. [27]

    H.-T. Ding, F. Karsch and S. Mukherjee,Thermodynamics of strong-interaction matter from Lattice QCD,Int. J. Mod. Phys. E24(2015) 1530007 [1504.05274]. 45

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  28. [28]

    Dynamical fluctuations in critical regime and across the 1st order phase transition

    L. Jiang, S. Wu and H. Song,Dynamical fluctuations in critical regime and across the 1st order phase transition,Nucl. Phys. A967(2017) 441 [1704.04765]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  29. [29]

    The QCD Phase Diagram from Statistical Model Analysis

    R. Stock, F. Becattini, M. Bleicher and J. Steinheimer,The QCD Phase Diagram from Statistical Model Analysis,Nucl. Phys. A982(2019) 827 [1811.07766]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  30. [30]

    Bzdak, S

    A. Bzdak, S. Esumi, V. Koch, J. Liao, M. Stephanov and N. Xu,Mapping the Phases of Quantum Chromodynamics with Beam Energy Scan,Phys. Rept.853(2020) 1 [1906.00936]

    work page arXiv 2020

  31. [31]

    Bluhm et al.,Dynamics of critical fluctuations: Theory – phenomenology – heavy-ion collisions,Nucl

    M. Bluhm et al.,Dynamics of critical fluctuations: Theory – phenomenology – heavy-ion collisions,Nucl. Phys. A1003(2020) 122016 [2001.08831]

    work page arXiv 2020

  32. [32]

    S. Wu, C. Shen and H. Song,Dynamically Exploring the QCD Matter at Finite Temperatures and Densities: A Short Review,Chin. Phys. Lett.38(2021) 081201 [2104.13250]

    work page arXiv 2021

  33. [33]

    Dore, J.M

    T. Dore, J.M. Karthein, I. Long, D. Mroczek, J. Noronha-Hostler, P. Parotto et al.,Critical lensing and kurtosis near a critical point in the QCD phase diagram in and out of equilibrium,Phys. Rev. D106(2022) 094024 [2207.04086]

    work page arXiv 2022

  34. [34]

    Fu, QCD at finite temperature and density within the fRG approach: an overview, Commun

    W.-j. Fu,QCD at finite temperature and density within the fRG approach: an overview, Commun. Theor. Phys.74(2022) 097304 [2205.00468]

    work page arXiv 2022

  35. [35]

    J. Li, L. Du and S. Shi,Rapidity scan approach for net-baryon cumulants with a statistical thermal model,Phys. Rev. C109(2024) 034906 [2311.11374]

    work page arXiv 2024

  36. [36]

    XU and M

    K. XU and M. HUANG,QCD critical end point and baryon number fluctuation,Nucl. Tech. 46(2024) 040005. [37]STARcollaboration,Precision Measurement of Net-Proton-Number Fluctuations in Au+Au Collisions at RHIC,Phys. Rev. Lett.135(2025) 142301 [2504.00817]

    work page arXiv 2024

  37. [37]

    B. Ling, T. Springer and M. Stephanov,Hydrodynamics of charge fluctuations and balance functions,Phys. Rev. C89(2014) 064901 [1310.6036]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  38. [38]

    Diffusive dynamics of critical fluctuations near the QCD critical point

    M. Nahrgang, M. Bluhm, T. Schaefer and S.A. Bass,Diffusive dynamics of critical fluctuations near the QCD critical point,Phys. Rev. D99(2019) 116015 [1804.05728]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  39. [39]

    Wu and H

    S. Wu and H. Song,Universal scaling of conserved charge in stochastic diffusion dynamics, Chin. Phys. C43(2019) 084103 [1903.06075]

    work page arXiv 2019

  40. [40]

    A. De, C. Plumberg and J.I. Kapusta,Calculating Fluctuations and Self-Correlations Numerically for Causal Charge Diffusion in Relativistic Heavy-Ion Collisions,Phys. Rev. C 102(2020) 024905 [2003.04878]

    work page arXiv 2020

  41. [41]

    Nahrgang and M

    M. Nahrgang and M. Bluhm,Modeling the diffusive dynamics of critical fluctuations near the QCD critical point,Phys. Rev. D102(2020) 094017 [2007.10371]. 46

    work page arXiv 2020

  42. [42]

    Chao and T

    J. Chao and T. Schaefer,N-particle irreducible actions for stochastic fluids,JHEP06(2023) 057 [2302.00720]

    work page arXiv 2023

  43. [43]

    Chattopadhyay, J

    C. Chattopadhyay, J. Ott, T. Schaefer and V. Skokov,Dynamic scaling of order parameter fluctuations in model B,Phys. Rev. D108(2023) 074004 [2304.07279]

    work page arXiv 2023

  44. [44]

    X. An, G. Ba¸ sar, M. Stephanov and H.-U. Yee,Evolution of Non-Gaussian Hydrodynamic Fluctuations,Phys. Rev. Lett.127(2021) 072301 [2009.10742]

    work page arXiv 2021

  45. [45]

    Real time evolution of non-Gaussian cumulants in the QCD critical regime

    S. Mukherjee, R. Venugopalan and Y. Yin,Real time evolution of non-Gaussian cumulants in the QCD critical regime,Phys. Rev. C92(2015) 034912 [1506.00645]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  46. [46]

    L. Du, X. An and U. Heinz,Baryon transport and the QCD critical point,Phys. Rev. C104 (2021) 064904 [2107.02302]

    work page arXiv 2021

  47. [47]

    When can long-range charge fluctuations serve as a QGP signal?

    E.V. Shuryak and M.A. Stephanov,When can long range charge fluctuations serve as a QGP signal?,Phys. Rev. C63(2001) 064903 [hep-ph/0010100]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  48. [48]

    Relation between baryon number fluctuations and experimentally observed proton number fluctuations in relativistic heavy ion collisions

    M. Kitazawa and M. Asakawa,Relation between baryon number fluctuations and experimentally observed proton number fluctuations in relativistic heavy ion collisions,Phys. Rev. C86(2012) 024904 [1205.3292]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  49. [49]

    Pradeep, K

    M. Pradeep, K. Rajagopal, M. Stephanov and Y. Yin,Freezing out fluctuations in Hydro+ near the QCD critical point,Phys. Rev. D106(2022) 036017 [2204.00639]

    work page arXiv 2022

  50. [50]

    Pradeep and M

    M.S. Pradeep and M. Stephanov,Maximum Entropy Freeze-Out of Hydrodynamic Fluctuations,Phys. Rev. Lett.130(2023) 162301 [2211.09142]

    work page arXiv 2023

  51. [51]

    An,Non-Gaussian Fluctuation Dynamics,Acta Phys

    X. An,Non-Gaussian Fluctuation Dynamics,Acta Phys. Polon. Supp.16(2023) 1 [2209.15005]

    work page arXiv 2023

  52. [52]

    Christov,On frame indifferent formulation of the maxwell–cattaneo model of finite-speed heat conduction,Mechanics Research Communications36(2009) 481

    C. Christov,On frame indifferent formulation of the maxwell–cattaneo model of finite-speed heat conduction,Mechanics Research Communications36(2009) 481

    2009

  53. [53]

    Lectures on non-equilibrium effective field theories and fluctuating hydrodynamics

    H. Liu and P. Glorioso,Lectures on non-equilibrium effective field theories and fluctuating hydrodynamics,PoSTASI2017(2018) 008 [1805.09331]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  54. [54]

    X. An, G. Basar, M. Stephanov and H.-U. Yee,Non-Gaussian fluctuation dynamics in relativistic fluids,Phys. Rev. C108(2023) 034910 [2212.14029]

    work page arXiv 2023

  55. [55]

    A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion

    Y. Akamatsu, A. Mazeliauskas and D. Teaney,A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion,Phys. Rev. C95(2017) 014909 [1606.07742]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  56. [56]

    X. An, G. Basar, M. Stephanov and H.-U. Yee,Relativistic Hydrodynamic Fluctuations, Phys. Rev. C100(2019) 024910 [1902.09517]

    work page arXiv 2019

  57. [57]

    Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation

    M.P. Heller and M. Spalinski,Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation,Phys. Rev. Lett.115(2015) 072501 [1503.07514]. 47

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  58. [58]

    Hohenberg and B.I

    P.C. Hohenberg and B.I. Halperin,Theory of Dynamic Critical Phenomena,Rev. Mod. Phys. 49(1977) 435

    1977

  59. [59]

    Dynamical evolution of critical fluctuations and its observation in heavy ion collisions

    M. Sakaida, M. Asakawa, H. Fujii and M. Kitazawa,Dynamical evolution of critical fluctuations and its observation in heavy ion collisions,Phys. Rev. C95(2017) 064905 [1703.08008]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  60. [60]

    Pihan, M

    G. Pihan, M. Bluhm, M. Kitazawa, T. Sami and M. Nahrgang,Critical net-baryon fluctuations in an expanding system,Phys. Rev. C107(2023) 014908 [2205.12834]

    work page arXiv 2023

  61. [61]

    Baryon Number, Strangeness and Electric Charge Fluctuations in QCD at High Temperature

    M. Cheng et al.,Baryon Number, Strangeness and Electric Charge Fluctuations in QCD at High Temperature,Phys. Rev. D79(2009) 074505 [0811.1006]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  62. [62]

    The QCD Equation of State to $\mathcal{O}(\mu_B^6)$ from Lattice QCD

    A. Bazavov et al.,The QCD Equation of State toO(µ 6 B)from Lattice QCD,Phys. Rev. D95 (2017) 054504 [1701.04325]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  63. [63]

    Higher-order baryon number susceptibilities: interplay between the chiral and the nuclear liquid-gas transitions

    A. Mukherjee, J. Steinheimer and S. Schramm,Higher-order baryon number susceptibilities: interplay between the chiral and the nuclear liquid-gas transitions,Phys. Rev. C96(2017) 025205 [1611.10144]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  64. [64]

    Parotto, M

    P. Parotto, M. Bluhm, D. Mroczek, M. Nahrgang, J. Noronha-Hostler, K. Rajagopal et al., QCD equation of state matched to lattice data and exhibiting a critical point singularity, Phys. Rev. C101(2020) 034901 [1805.05249]

    work page arXiv 2020

  65. [65]

    Schofield,Parametric Representation of the Equation of State Near A Critical Point, Phys

    P. Schofield,Parametric Representation of the Equation of State Near A Critical Point, Phys. Rev. Lett.22(1969) 606

    1969

  66. [66]

    Josephson,Equation of state near the critical point,Journal of Physics C: Solid State Physics2(1969) 1113

    B.D. Josephson,Equation of state near the critical point,Journal of Physics C: Solid State Physics2(1969) 1113

    1969

  67. [67]

    Search for the QCD Critical Point in High Energy Nuclear Collisions: A Status Report

    Y. Zhang, Z. Wang, X. Luo and N. Xu,Search for the QCD Critical Point in High Energy Nuclear Collisions: A Status Report,Eur. Phys. J. Spec. Top.(2026) [arXiv:2602.08356 [nucl-ex]]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  68. [68]

    S. Wu, Z. Wu and H. Song,Universal scaling of theσfield and net-protons from Langevin dynamics of model A,Phys. Rev. C99(2019) 064902 [1811.09466]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  69. [69]

    Wu,Dynamics of the conserved net-baryon density near the QCD critical point within an inhomogeneous quark-gluon plasma profile,Phys

    S. Wu,Dynamics of the conserved net-baryon density near the QCD critical point within an inhomogeneous quark-gluon plasma profile,Phys. Rev. C111(2025) 014915 [2406.12325]

    work page arXiv 2025

  70. [70]

    X. An, G. Basar, M. Stephanov and H.-U. Yee,Relativistic fluctuations in stochastic fluid dynamics,EPJ Web Conf.296(2024) 13011 [2402.18727]

    work page arXiv 2024

  71. [71]

    X. An, G. Basar and M. Stephanov,Non-Gaussian fluctuations in relativistic hydrodynamics: Confluent equations for three-point correlations, 4, 2026. 48

    2026

  72. [72]

    Non-Gaussian hydrodynamic fluctuations in an expanding relativistic fluid

    G. Basar and S. Song,Non-Gaussian hydrodynamic fluctuations in an expanding relativistic fluid,2604.27730

    work page internal anchor Pith review Pith/arXiv arXiv

  73. [73]

    An and M

    X. An and M. Spali´ nski,QGP physics from attractor perturbations,Phys. Rev. D110(2024) 114043 [2312.17237]

    work page arXiv 2024

  74. [74]

    N. Oei, N. Krenz, H. van Hees, C. Greiner and J.M. Torres-Rincon,Formation, dissociation, and regeneration of charmonia within microscopic Langevin simulations,Phys. Rev. D111 (2025) 074012 [2410.19619]

    work page arXiv 2025

  75. [75]

    Rajagopal, B

    K. Rajagopal, B. Scheihing-Hitschfeld and U.A. Wiedemann,Universal Equilibration Condition for Heavy Quarks,Phys. Rev. Lett.135(2025) 242301 [2504.21139]

    work page arXiv 2025

  76. [76]

    Liu, W.-J

    F.-L. Liu, W.-J. Xing, X.-Y. Wu, G.-Y. Qin, S. Cao and X.-N. Wang,QLBT: a linear Boltzmann transport model for heavy quarks in a quark-gluon plasma of quasi-particles,Eur. Phys. J. C82(2022) 350 [2107.11713]

    work page arXiv 2022

  77. [77]

    Schlichting, D

    S. Schlichting, D. Smith and L. von Smekal,Spectral functions and critical dynamics of the O(4) model from classical-statistical lattice simulations,Nucl. Phys. B950(2020) 114868 [1908.00912]

    work page arXiv 2020

  78. [78]

    Florio, E

    A. Florio, E. Grossi, A. Mazeliauskas, A. Soloviev and D. Teaney,Supercooled Goldstone Bosons at the QCD Chiral Phase Transition,Phys. Rev. Lett.135(2025) 242303 [2504.03516]

    work page arXiv 2025

  79. [79]

    Aarts, K

    G. Aarts, K. Fukushima, T. Hatsuda, A. Ipp, S. Shi, L. Wang et al.,Physics-driven learning for inverse problems in quantum chromodynamics,Nature Rev. Phys.7(2025) 154 [2501.05580]

    work page arXiv 2025

  80. [80]

    Zhu, L.-Q

    D.-X. Zhu, L.-Q. Zhu, X. Chen, D.-F. Hou and K. Zhou,Neural-Network Holographic Model of the QCD Phase Transition under Lattice and HRG Constraints,2603.25571

    work page arXiv

Showing first 80 references.