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arxiv: 2604.04533 · v1 · submitted 2026-04-06 · ⚛️ nucl-th · hep-ph

Recognition: no theorem link

Dissipative spin hydrodynamics in Bjorken flow and thermal dilepton production

Sejal Singh , Sourav Dey , Arpan Das , Hiranmaya Mishra , Amaresh Jaiswal
Authors on Pith no claims yet

Pith reviewed 2026-05-10 19:54 UTC · model grok-4.3

classification ⚛️ nucl-th hep-ph
keywords spin hydrodynamicsBjorken flowthermal dileptonsquark-gluon plasmaviscous hydrodynamicsspin transportboost-invariant expansion
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The pith

Spin dynamics in expanding plasma modifies temperature and increases thermal dilepton production compared to standard viscous hydrodynamics.

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

The paper studies boost-invariant expansion using a first-order spin hydrodynamic model where the spin chemical potential enters at leading order alongside viscous terms. It derives coupled equations for temperature and spin chemical potential components under a symmetric energy-momentum tensor and separately conserved spin tensor. Only magnetic-like spin components survive in this flow, with transverse ones decaying faster due to spin dissipation while the longitudinal component lasts longer. These spin effects alter the cooling history of the medium, which in turn raises the rate of quark-antiquark annihilation into dileptons above the yield obtained from dissipative hydrodynamics without spin. A reader would care because dileptons can escape the plasma and carry information about internal spin transport that other signals may miss.

Core claim

Within the first-order spin hydrodynamic framework applied to Bjorken flow, the evolution of magnetic-like spin chemical potential components depends on spin transport coefficients and modifies the medium temperature profile, resulting in higher thermal dilepton yields from quark-antiquark annihilation than those predicted by standard dissipative hydrodynamics alone, with the size of the increase controlled by the values of the spin diffusion coefficients.

What carries the argument

The coupled evolution equations for medium temperature and independent components of the spin chemical potential, restricted to surviving magnetic-like components in boost-invariant flow, where spin dissipation causes faster decay of transverse components.

If this is right

  • Thermal dileptons can serve as an indirect probe of spin dynamics and spin transport coefficients in the quark-gluon plasma.
  • The magnitude of the dilepton yield enhancement scales directly with the specific values chosen for the spin transport coefficients.
  • The longitudinal spin chemical potential component persists longer than transverse components, influencing dilepton production at later stages of the expansion.
  • The temperature evolution deviates from pure viscous hydrodynamics once spin degrees of freedom are included.

Where Pith is reading between the lines

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

  • Dilepton data from heavy-ion collisions could be reanalyzed to place bounds on spin transport coefficients if the enhancement is confirmed.
  • The same spin-modified temperature profiles would likely affect other electromagnetic observables such as direct photons.
  • Extending the framework beyond boost invariance could reveal how spin effects behave in more realistic, non-central collision geometries.

Load-bearing premise

The spin chemical potential can be treated as a leading-order hydrodynamic variable throughout the expansion inside a first-order theory that uses a symmetric energy-momentum tensor and assumes the spin tensor is conserved independently.

What would settle it

A measured dilepton invariant-mass spectrum that matches the yield calculated from standard dissipative hydrodynamics with no additional enhancement from spin-modified temperature profiles.

Figures

Figures reproduced from arXiv: 2604.04533 by Amaresh Jaiswal, Arpan Das, Hiranmaya Mishra, Sejal Singh, Sourav Dey.

Figure 1
Figure 1. Figure 1: FIG. 1. Proper time evolution of the medium temperature [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. We show the evolution of different components of the [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Dilepton production rate as a function of transverse [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Dilepton production rate as a function of trans [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
read the original abstract

We investigate the boost-invariant expansion of a recently developed first-order spin hydrodynamic framework in which the spin chemical potential is treated as a leading-order hydrodynamic variable. Considering a symmetric energy-momentum tensor and a separately conserved spin tensor, we derive the coupled evolution equations for the medium temperature and the independent components of the spin chemical potential in the presence of both viscous and spin-diffusive transport coefficients. For a boost-invariant system, only the magnetic-like components of the spin chemical potential survive, and their evolution is shown to depend sensitively on the spin transport coefficients. The transverse spin components decay more rapidly due to spin dissipation, while the longitudinal component survives for a longer duration. We further demonstrate that the evolution of the spin degrees of freedom modifies the temperature profile of the expanding medium. Using the resulting temperature profiles, we calculate thermal dilepton production rates from quark-antiquark annihilation. We find that the presence of spin dynamics enhances the dilepton yield relative to standard dissipative hydrodynamics, with the magnitude of the enhancement depending on the spin transport coefficients. Our results indicate that thermal dileptons can provide an indirect probe of spin dynamics and spin transport in the quark-gluon plasma.

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 manuscript develops a first-order dissipative spin hydrodynamics framework for boost-invariant Bjorken flow, treating the spin chemical potential as a leading-order variable with a symmetric energy-momentum tensor and separately conserved spin tensor. It derives coupled evolution equations for the medium temperature T(τ) and the surviving magnetic-like components of the spin chemical potential, demonstrates that spin dissipation modifies the temperature profile, and computes the resulting thermal dilepton yield from quark-antiquark annihilation, finding an enhancement relative to standard viscous hydrodynamics whose magnitude depends on the spin transport coefficients.

Significance. If the hydrodynamic ordering holds, the work provides a concrete link between spin transport and an electromagnetic observable, offering a potential indirect probe of spin dynamics in the QGP. The explicit derivation of the coupled T(τ) and μ_s equations and the demonstration of back-reaction on the temperature profile are strengths that make the result falsifiable once specific spin transport coefficients are fixed.

major comments (2)
  1. [Bjorken flow section (coupled evolution equations for T(τ) and μ_s)] The central claim that spin dynamics modifies the temperature profile and enhances the dilepton yield rests on the validity of the coupled evolution equations throughout the expansion. However, in boost-invariant Bjorken flow the initial expansion rate 1/τ diverges as τ→0+, so the Knudsen number in the spin sector is not parametrically small; the assumption that the spin chemical potential remains O(1) while spin diffusion is O(∂) may break down at early times, rendering the reported temperature modification unreliable. This issue is load-bearing for the dilepton enhancement result.
  2. [Dilepton production rate calculation (temperature profiles and rate integral)] The enhancement of the dilepton yield is stated to depend on the spin transport coefficients, yet the manuscript provides neither explicit functional forms or numerical values for these coefficients nor sensitivity studies showing how the yield changes across plausible ranges. Without such checks, it is unclear whether the enhancement survives when the coefficients are varied consistently with the first-order framework.
minor comments (1)
  1. [Abstract] The abstract claims that 'only the magnetic-like components of the spin chemical potential survive' but does not define the decomposition into magnetic-like versus other components or state the initial conditions used for the longitudinal and transverse modes.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment point by point below, providing the strongest honest defense of our results while acknowledging where clarifications or additions are warranted.

read point-by-point responses

  1. Referee: [Bjorken flow section (coupled evolution equations for T(τ) and μ_s)] The central claim that spin dynamics modifies the temperature profile and enhances the dilepton yield rests on the validity of the coupled evolution equations throughout the expansion. However, in boost-invariant Bjorken flow the initial expansion rate 1/τ diverges as τ→0+, so the Knudsen number in the spin sector is not parametrically small; the assumption that the spin chemical potential remains O(1) while spin diffusion is O(∂) may break down at early times, rendering the reported temperature modification unreliable. This issue is load-bearing for the dilepton enhancement result.

    Authors: We agree that the formal divergence of the expansion rate as τ→0+ challenges the hydrodynamic ordering at the absolute earliest times. However, our numerical implementation of the coupled evolution equations begins at a finite initial proper time τ₀ (chosen such that the Knudsen number remains small, consistent with standard practice in Bjorken-flow hydrodynamics). The spin chemical potential is initialized at this τ₀ and evolves forward; the back-reaction on T(τ) and the resulting dilepton yield are therefore computed only in the regime where the first-order spin-hydrodynamic ordering is under control. We will revise the manuscript to state the specific τ₀ employed, to display the Knudsen number evolution explicitly, and to add a short paragraph discussing the domain of validity of the framework. revision: partial

  2. Referee: [Dilepton production rate calculation (temperature profiles and rate integral)] The enhancement of the dilepton yield is stated to depend on the spin transport coefficients, yet the manuscript provides neither explicit functional forms or numerical values for these coefficients nor sensitivity studies showing how the yield changes across plausible ranges. Without such checks, it is unclear whether the enhancement survives when the coefficients are varied consistently with the first-order framework.

    Authors: We accept that the dependence on the spin transport coefficients must be made quantitative. In the revised version we will specify the numerical values (or functional forms) of the spin diffusion and relaxation coefficients used in our benchmark calculations, drawing from existing kinetic-theory and holographic estimates. We will also include a dedicated sensitivity study in which these coefficients are varied over a range still compatible with the first-order dissipative ordering, and we will show the corresponding dilepton spectra. This will demonstrate that the reported enhancement persists for physically motivated choices of the coefficients. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper starts from conservation of a symmetric energy-momentum tensor and a separately conserved spin tensor, derives the coupled evolution equations for temperature and the surviving magnetic-like components of the spin chemical potential in Bjorken flow, solves them with spin transport coefficients supplied as external inputs, and integrates the resulting temperature profiles to obtain dilepton yields. The enhancement is stated to depend on the values of those coefficients rather than being forced by the equations themselves. No self-definitional steps, fitted inputs relabeled as predictions, or load-bearing self-citations that reduce the central result to its own inputs are present in the provided abstract or summary. The modeling choice to treat the spin chemical potential as leading-order is an explicit assumption of the framework, not a circular derivation.

Axiom & Free-Parameter Ledger

1 free parameters · 3 axioms · 0 invented entities

Abstract-only information limits the ledger to explicitly stated modeling choices; the framework is described as recently developed, so many background assumptions are inherited rather than derived here.

free parameters (1)
  • spin transport coefficients
    The evolution of spin chemical potential components and the resulting dilepton enhancement are stated to depend sensitively on these coefficients, but no numerical values or fitting procedure are given in the abstract.
axioms (3)
  • domain assumption Spin chemical potential treated as leading-order hydrodynamic variable
    Explicitly stated as the basis of the recently developed first-order spin hydrodynamic framework.
  • domain assumption Symmetric energy-momentum tensor and separately conserved spin tensor
    Stated as the setup for deriving the coupled evolution equations.
  • domain assumption Boost-invariant Bjorken flow geometry
    Used to reduce the system so that only magnetic-like spin components survive.

pith-pipeline@v0.9.0 · 5518 in / 1370 out tokens · 30483 ms · 2026-05-10T19:54:42.521269+00:00 · methodology

discussion (0)

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Forward citations

Cited by 2 Pith papers

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

  1. Exact expectation values in a boost-invariant fluid of Dirac fermions with finite spin density

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    Exact calculations in a boost-invariant free Dirac fermion fluid show spin polarization arises only from finite spin potential, with shear-induced polarization and spin Hall effect absent.

  2. 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

Works this paper leans on

89 extracted references · 65 canonical work pages · cited by 2 Pith papers

  1. [1]

    Moreover, in the limit ω αβ → 0, one obtains P (T, ω µν ) = P0(T ), which is the pressure for the spin-less fluid

    Note that in our calculation both T , and ω µν are leading order in the hydrodynamic gradient ex- pansion, hence P (T, ω µν ) ∼ O (1). Moreover, in the limit ω αβ → 0, one obtains P (T, ω µν ) = P0(T ), which is the pressure for the spin-less fluid. Using the expression of P (T, ω µν ) in Eq. (

  2. [2]

    For a baryon free system and for Bjorken flow hµ identically vanishes

    one finds, Sµν (T, ω µν ) = ∂P ∂ω µν ⏐ ⏐ ⏐ ⏐ T = S0(T )ω µν , (23) − κ 11 Sαβ ε+P ∇ µ (βω αβ ) − κ 12∇ µ α [47]. For a baryon free system and for Bjorken flow hµ identically vanishes. Naturally, one can apply the Landau frame condition. 2 Here we have not incorporated higher order terms in ω µν ω µν , e.g., ( ω µν ω µν )2, because we consider ω µν /T small....

  3. [3]

    is the projection of ∂µ T µν = 0 along the direc- tion of uµ . Eq. ( 27) is the projection of ∂µ T µν = 0 nor- mal to the the direction of uµ , i.e., ∆ α ν ∂µ T µν = 0. The third equation (Eq. ( 28)) is nothing but the conservation of the total angular momentum tensor. Note that in our calculation, we consider a symmetric energy-momentum tensor, hence ∂µ ...

  4. [4]

    (42) The condition S0i FC = 0 (for i = 1, 2, 3) implies CκX = 0, CκY = 0, and CκZ = 0, i.e., κ µ = 0

    S0i FC (for i = 1 , 2, 3) can be expressed as [ 52], S01 FC = − 2πR 2τ S0 CκX sinh ( ηFC 2 ) , (40) S02 FC = − 2πR 2τ S0CκY sinh ( ηFC 2 ) (41) S03 FC = − πR 2τ S0CκZ ηFC. (42) The condition S0i FC = 0 (for i = 1, 2, 3) implies CκX = 0, CκY = 0, and CκZ = 0, i.e., κ µ = 0. Therefore, for the boost invariant system, the electric-like components (κ µ ) of t...

  5. [5]

    in Eqs. (22), (24), and (25) the equilibrium thermodynamic quantities can be expressed as, P (T, ω µν ) = P0(T ) + S0(T ) C2, (48) ε(T, ω µν ) = ε0(T ) + [ S0(T ) + T S′ 0(T ) ] C2, (49) s(T, ω µν ) = s0(T ) + S′ 0(T )C2. (50) IV. SPIN HYDRODYNAMIC EQUATIONS FOR A BOOST-INV ARIANT SYSTEM For a boost invariant system, Eq. ( 27) is trivially satis- fied (see...

  6. [6]

    No non-trivial equations are obtained when we contract Eq

    with Xα uβ , Yα uβ , Zα uβ , Xα Yβ , Xα Zβ , and Yα Zβ . No non-trivial equations are obtained when we contract Eq. ( 52) with Xα uβ , Yα uβ , and Zα uβ . How- ever, when we contract Eq. ( 52) with Yα Zβ , Xα Zβ , and Xα Yβ we find the proper time evolution of CωX , CωY , and CωZ , respectively (see Appendix B for details), dCωX dτ + CωX ( S′ 0(T ) S0(T ) ...

    2019

  7. [7]

    Appendix B: Derivation of Eqs

    is trivially satisfied. Appendix B: Derivation of Eqs. (61)-(63) Contracting Eq. ( 52) with uα Xβ one finds, uα Xβ [ ∂S αβ ∂τ + Sαβ τ + ∂µ Sµαβ (1) ] = 0. (B1) Now, uα Xβ ∂S αβ ∂τ = ∂ ∂τ [ uα Xβ Sαβ ] = ∂ ∂τ [ S0(T )uα Xβ ω αβ ] = ∂ ∂τ [ S0(T )uα Xβ ǫαβγδ uγ ω δ ] = 0. (B2) Similarly it can be shown that, uα Xβ Sαβ = 0. Moreover, uα Xβ ∂µ Sµαβ (1) = uα Xβ ∂...

  8. [8]

    Global $\Lambda$ hyperon polarization in nuclear collisions: evidence for the most vortical fluid

    STAR Collaboration, L. Adamczyk et al. , “Global Λ hyperon polarization in nuclear collisions: evidence for the most vortical fluid,” Nature 548 (2017) 62–65 , arXiv:1701.06657 [nucl-ex]

    work page Pith review arXiv 2017

  9. [9]

    Adamet al.(STAR), Phys

    STAR Collaboration, J. Adam et al. , “Global polarization of Λ hyperons in Au+Au collisions at √ sN N = 200 GeV,” Phys. Rev. C 98 (2018) 014910 , arXiv:1805.04400 [nucl-ex]

    work page arXiv 2018

  10. [10]

    Adamet al.(STAR), Phys

    STAR Collaboration, J. Adam et al. , “Polarization of Λ ( ¯Λ) hyperons along the beam direction in Au+Au collisions at √ sN N = 200 GeV,” Phys. Rev. Lett. 123 no. 13, (2019) 132301 , arXiv:1905.11917 [nucl-ex]

    work page arXiv 2019

  11. [11]

    Acharyaet al.(ALICE), Phys

    ALICE Collaboration, S. Acharya et al. , “Global polarization of Λ ¯Λ hyperons in Pb-Pb collisions at√ sN N = 2.76 and 5.02 TeV,” Phys. Rev. C 101 no. 4, (2020) 044611 , arXiv:1909.01281 [nucl-ex]

    work page arXiv 2020

  12. [12]

    Λ Polarization in Au+Au Collisions at √ sN N = 2. 4 GeV Measured with HADES,

    HADES Collaboration, F. J. Kornas, “Λ Polarization in Au+Au Collisions at √ sN N = 2. 4 GeV Measured with HADES,” Springer Proc. Phys. 250 (2020) 435–439

    2020

  13. [13]

    Globally Polarized Quark-gluon Plasma in Non-central A+A Collisions

    Z.-T. Liang and X.-N. Wang, “Globally polarized quark-gluon plasma in non-central A+A collisions,” Phys. Rev. Lett. 94 (2005) 102301 , arXiv:nucl-th/0410079 [nucl-th] . [Erratum: Phys. Rev. Lett.96,039901(2006)]

    work page Pith review arXiv 2005

  14. [14]

    Angular momentum conservation in heavy ion collisions at very high energy

    F. Becattini, F. Piccinini, and J. Rizzo, “Angular momentum conservation in heavy ion collisions at very high energy,” Phys. Rev. C77 (2008) 024906 , arXiv:0711.1253 [nucl-th]

    work page Pith review arXiv 2008

  15. [15]

    Global quark polarization in non-central A+A collisions,

    J.-H. Gao, S.-W. Chen, W.-T. Deng, Z.-T. Liang, Q. Wang, and X.-N. Wang, “Global quark polarization in non-central A+A collisions,” Phys. Rev. C77 (2008) 044902 , arXiv:0710.2943 [nucl-th]

    work page arXiv 2008

  16. [16]

    Quark Polarization in a Viscous Quark-Gluon Plasma,

    X.-G. Huang, P. Huovinen, and X.-N. Wang, “Quark Polarization in a Viscous Quark-Gluon Plasma,” Phys. Rev. C 84 (2011) 054910 , arXiv:1108.5649 [nucl-th]

    work page arXiv 2011

  17. [17]

    Relativistic distribution function for particles with spin at local thermodynamical equilibrium

    F. Becattini, V. Chandra, L. Del Zanna, and E. Grossi, “Relativistic distribution function for particles with spin at local thermodynamical equilibrium,” Annals Phys. 338 (2013) 32–49 , arXiv:1303.3431 [nucl-th]

    work page Pith review arXiv 2013

  18. [18]

    Polarization of massive fermions in a vortical fluid,

    R.-H. Fang, L.-G. Pang, Q. Wang, and X.-N. Wang, “Polarization of massive fermions in a vortical fluid,” Phys. Rev. C94 no. 2, (2016) 024904 , arXiv:1604.04036 [nucl-th]

    work page arXiv 2016

  19. [19]

    Polarized secondary particles in unpolarized high energy hadron-hadron collisions?,

    S. A. Voloshin, “Polarized secondary particles in unpolarized high energy hadron-hadron collisions?,” arXiv:nucl-th/0410089 [nucl-th]

    work page arXiv

  20. [20]

    Polarization probes of vorticity in heavy ion collisions,

    B. Betz, M. Gyulassy, and G. Torrieri, “Polarization probes of vorticity in heavy ion collisions,” Phys. Rev. C76 (2007) 044901 , arXiv:0708.0035 [nucl-th]

    work page arXiv 2007

  21. [21]

    Becattini, G

    F. Becattini, G. Inghirami, V. Rolando, A. Beraudo, L. Del Zanna, A. De Pace, M. Nardi, G. Pagliara, and V. Chandra, “A study of vorticity formation in high energy nuclear collisions,” Eur. Phys. J. C75 no. 9, (2015) 406 , arXiv:1501.04468 [nucl-th] . [Erratum: Eur. Phys. J.C78,no.5,354(2018)]

    work page arXiv 2015

  22. [22]

    Spin and polarization: a new direction in relativistic heavy ion physics,

    F. Becattini, “Spin and polarization: a new direction i n relativistic heavy ion physics,” Rept. Prog. Phys. 85 no. 12, (2022) 122301 , arXiv:2204.01144 [nucl-th]

    work page arXiv 2022

  23. [23]

    Relativistic viscous hydrodynamics for heavy-ion collisions with ECHO-QGP

    L. Del Zanna, V. Chandra, G. Inghirami, V. Rolando, A. Beraudo, A. De Pace, G. Pagliara, A. Drago, and F. Becattini, “Relativistic viscous hydrodynamics for heavy-ion collisions with ECHO-QGP,” Eur. Phys. J. C 73 (2013) 2524 , arXiv:1305.7052 [nucl-th]

    work page Pith review arXiv 2013

  24. [24]

    A 3+1 dimensional viscous hydrodynamic code for relativistic heavy ion collisions

    I. Karpenko, P. Huovinen, and M. Bleicher, “A 3+1 dimensional viscous hydrodynamic code for relativistic heavy ion collisions,” Comput. Phys. Commun. 185 (2014) 3016–3027 , arXiv:1312.4160 [nucl-th]

    work page Pith review arXiv 2014

  25. [25]

    Estimates of hyperon polarization in heavy-ion collisions at collision energies √sN N = 4–40 GeV,

    Y. B. Ivanov, V. D. Toneev, and A. A. Soldatov, “Estimates of hyperon polarization in heavy-ion collisions at collision energies √ sN N = 4–40 GeV,” Phys. Rev. C 100 no. 1, (2019) 014908 , arXiv:1903.05455 [nucl-th]

    work page arXiv 2019

  26. [26]

    Global $\Lambda$ polarization in heavy-ion collisions from a transport model

    H. Li, L.-G. Pang, Q. Wang, and X.-L. Xia, “Global Λ polarization in heavy-ion collisions from a transport model,” Phys. Rev. C96 no. 5, (2017) 054908 , arXiv:1704.01507 [nucl-th]

    work page Pith review arXiv 2017

  27. [27]

    Is different Λ and ¯Λ polarization caused by different spatio-temporal freeze-out picture?,

    O. Vitiuk, L. V. Bravina, and E. E. Zabrodin, “Is different Λ and ¯Λ polarization caused by different spatio-temporal freeze-out picture?,” Phys. Lett. B 803 (2020) 135298 , arXiv:1910.06292 [hep-ph]

    work page arXiv 2020

  28. [28]

    Lambda hyperon polarization in relativistic heavy ion collisions from the chiral kinetic approach

    Y. Sun and C. M. Ko, “Λ hyperon polarization in relativistic heavy ion collisions from a chiral kinetic approach,” Phys. Rev. C96 no. 2, (2017) 024906 , arXiv:1706.09467 [nucl-th]

    work page Pith review arXiv 2017

  29. [29]

    Polarization and Vorticity in the Quark–Gluon Plasma,

    F. Becattini and M. A. Lisa, “Polarization and Vorticit y in the Quark–Gluon Plasma,” Ann. Rev. Nucl. Part. Sci. 70 (2020) 395–423 , arXiv:2003.03640 [nucl-ex]

    work page arXiv 2020

  30. [30]

    Spin-thermal shear coupling in a relativistic fluid,

    F. Becattini, M. Buzzegoli, and A. Palermo, “Spin-thermal shear coupling in a relativistic fluid,” Phys. Lett. B 820 (2021) 136519 , arXiv:2103.10917 [nucl-th]

    work page arXiv 2021

  31. [31]

    Spin polarization induced by the hydrodynamic gradients,

    S. Y. F. Liu and Y. Yin, “Spin polarization induced by the hydrodynamic gradients,” JHEP 07 (2021) 188 , arXiv:2103.09200 [hep-ph]

    work page arXiv 2021

  32. [32]

    Local Polarization and Isothermal Local Equilibrium in Relativistic Heavy Ion Collisions,

    F. Becattini, M. Buzzegoli, G. Inghirami, I. Karpenko, and A. Palermo, “Local Polarization and Isothermal Local Equilibrium in Relativistic Heavy Ion Collisions,” Phys. Rev. Lett. 127 no. 27, (2021) 272302 , arXiv:2103.14621 [nucl-th]

    work page arXiv 2021

  33. [33]

    Shear-Induced Spin Polarization in Heavy-Ion Collisions,

    B. Fu, S. Y. F. Liu, L. Pang, H. Song, and Y. Yin, “Shear-Induced Spin Polarization in Heavy-Ion Collisions,” Phys. Rev. Lett. 127 no. 14, (2021) 142301 , arXiv:2103.10403 [hep-ph]

    work page arXiv 2021

  34. [34]

    Relativistic hydrodynamics for spin-polarized fluids,

    W. Florkowski, A. Kumar, and R. Ryblewski, “Relativistic hydrodynamics for spin-polarized fluids,” Prog. Part. Nucl. Phys. 108 (2019) 103709 , arXiv:1811.04409 [nucl-th]

    work page arXiv 2019

  35. [35]

    Thermodynamic versus kinetic approach to polarization-vorticity coupling

    W. Florkowski, A. Kumar, and R. Ryblewski, “Thermodynamic versus kinetic approach to 16 polarization-vorticity coupling,” Phys. Rev. C98 (2018) 044906 , arXiv:1806.02616 [hep-ph]

    work page Pith review arXiv 2018

  36. [36]

    Spin-dependent distribution functions for relativistic hydrodynamics of spin-1/2 particles

    W. Florkowski, B. Friman, A. Jaiswal, R. Ryblewski, and E. Speranza, “Spin-dependent distribution functions for relativistic hydrodynamics of spin-1/2 particles,” Phys. Rev. D97 no. 11, (2018) 116017 , arXiv:1712.07676 [nucl-th]

    work page Pith review arXiv 2018

  37. [37]

    Relativistic fluid dynamics with spin

    W. Florkowski, B. Friman, A. Jaiswal, and E. Speranza, “Relativistic fluid dynamics with spin,” Phys. Rev. C97 no. 4, (2018) 041901 , arXiv:1705.00587 [nucl-th]

    work page Pith review arXiv 2018

  38. [38]

    Spin polarization evolution in a boost invariant hydrodynamical background

    W. Florkowski, A. Kumar, R. Ryblewski, and R. Singh, “Spin polarization evolution in a boost invariant hydrodynamical background,” Phys. Rev. C99 no. 4, (2019) 044910 , arXiv:1901.09655 [hep-ph]

    work page Pith review arXiv 2019

  39. [39]

    Longitudinal spin polarization in a thermal model,

    W. Florkowski, A. Kumar, R. Ryblewski, and A. Mazeliauskas, “Longitudinal spin polarization in a thermal model,” Phys. Rev. C100 no. 5, (2019) 054907 , arXiv:1904.00002 [nucl-th]

    work page arXiv 2019

  40. [40]

    Fate of spin polarization in a relativistic fluid: An entropy-current analysis

    K. Hattori, M. Hongo, X.-G. Huang, M. Matsuo, and H. Taya, “Fate of spin polarization in a relativistic fluid: An entropy-current analysis,” Phys. Lett. B795 (2019) 100–106 , arXiv:1901.06615 [hep-th]

    work page Pith review arXiv 2019

  41. [41]

    Spin hydrodynamics and symmetric energy-momentum tensors – A current induced by the spin vorticity –,

    K. Fukushima and S. Pu, “Spin hydrodynamics and symmetric energy-momentum tensors – A current induced by the spin vorticity –,” Phys. Lett. B 817 (2021) 136346 , arXiv:2010.01608 [hep-th]

    work page arXiv 2021

  42. [42]

    Nondissipative Second-Order Transport, Spin, and Pseudogauge Transformations in Hydrodynamics,

    S. Li, M. A. Stephanov, and H.-U. Yee, “Nondissipative Second-Order Transport, Spin, and Pseudogauge Transformations in Hydrodynamics,” Phys. Rev. Lett. 127 no. 8, (2021) 082302 , arXiv:2011.12318 [hep-th]

    work page arXiv 2021

  43. [43]

    Relativistic viscous hydrodynamics with angular momentum,

    D. She, A. Huang, D. Hou, and J. Liao, “Relativistic viscous hydrodynamics with angular momentum,” Sci. Bull. 67 (2022) 2265–2268 , arXiv:2105.04060 [nucl-th]

    work page arXiv 2022

  44. [44]

    Sound waves and vortices in a polarized relativistic fluid

    D. Montenegro, L. Tinti, and G. Torrieri, “Sound waves and vortices in a polarized relativistic fluid,” Phys. Rev. D96 no. 7, (2017) 076016 , arXiv:1703.03079 [hep-th]

    work page Pith review arXiv 2017

  45. [45]

    The ideal relativistic fluid limit for a medium with polarization

    D. Montenegro, L. Tinti, and G. Torrieri, “The ideal relativistic fluid limit for a medium with polarization,” Phys. Rev. D96 no. 5, (2017) 056012 , arXiv:1701.08263 [hep-th]

    work page Pith review arXiv 2017

  46. [46]

    Perfect-fluid hydrodynamics with constant acceleration along the stream lines and spin polarization

    W. Florkowski, E. Speranza, and F. Becattini, “Perfect-fluid hydrodynamics with constant acceleration along the stream lines and spin polarization,” Acta Phys. Polon. B49 (2018) 1409 , arXiv:1803.11098 [nucl-th]

    work page Pith review arXiv 2018

  47. [47]

    Relativistic dissipative spin dynamics in the relaxation time approximation,

    S. Bhadury, W. Florkowski, A. Jaiswal, A. Kumar, and R. Ryblewski, “Relativistic dissipative spin dynamics in the relaxation time approximation,” Phys. Lett. B 814 (2021) 136096 , arXiv:2002.03937 [hep-ph]

    work page arXiv 2021

  48. [48]

    From Chiral Kinetic Theory To Spin Hydrodynamics,

    S. Shi, C. Gale, and S. Jeon, “From Chiral Kinetic Theory To Spin Hydrodynamics,” Nucl. Phys. A 1005 (2021) 121949 , arXiv:2002.01911 [nucl-th]

    work page arXiv 2021

  49. [49]

    Relativistic second-order dissipative spin hydrodynamics from the method of moments,

    N. Weickgenannt, D. Wagner, E. Speranza, and D. H. Rischke, “Relativistic second-order dissipative spin hydrodynamics from the method of moments,” Phys. Rev. D 106 no. 9, (2022) 096014 , arXiv:2203.04766 [nucl-th]

    work page arXiv 2022

  50. [50]

    Kinetic theory for massive spin-1/2 particles from the Wigner-function formalism,

    N. Weickgenannt, X.-L. Sheng, E. Speranza, Q. Wang, and D. H. Rischke, “Kinetic theory for massive spin-1/2 particles from the Wigner-function formalism,” arXiv:1902.06513 [hep-ph]

    work page arXiv 1902

  51. [51]

    Generating Spin Polarization from Vorticity through Nonlocal Collisions,

    N. Weickgenannt, E. Speranza, X.-l. Sheng, Q. Wang, and D. H. Rischke, “Generating Spin Polarization from Vorticity through Nonlocal Collisions,” Phys. Rev. Lett. 127 no. 5, (2021) 052301 , arXiv:2005.01506 [hep-ph]

    work page arXiv 2021

  52. [52]

    Spin dynamics with realistic hydrodynamic background for relativistic heavy-ion collisions,

    S. K. Singh, R. Ryblewski, and W. Florkowski, “Spin dynamics with realistic hydrodynamic background for relativistic heavy-ion collisions,” Phys. Rev. C 111 no. 2, (2025) 024907 , arXiv:2411.08223 [hep-ph]

    work page arXiv 2025

  53. [53]

    Spin polarization of Λ hyperons from dissipative spin hydrodynamics,

    Sapna, S. K. Singh, and D. Wagner, “Spin polarization of Λ hyperons from dissipative spin hydrodynamics,” Phys. Rev. C 112 no. 5, (2025) 054902 , arXiv:2503.22552 [hep-ph]

    work page arXiv 2025

  54. [54]

    Kubo formula for spin hydrodynamics: Spin chemical potential as the leading order term in a gradient expansion,

    S. Dey and A. Das, “Kubo formula for spin hydrodynamics: Spin chemical potential as the leading order term in a gradient expansion,” Phys. Rev. D 111 no. 7, (2025) 074037 , arXiv:2410.04141 [nucl-th]

    work page arXiv 2025

  55. [55]

    Analytic solutions of relativistic dissipative spin hydrodynamics with Bjorken expansion,

    D.-L. Wang, S. Fang, and S. Pu, “Analytic solutions of relativistic dissipative spin hydrodynamics with Bjorken expansion,” Phys. Rev. D 104 no. 11, (2021) 114043 , arXiv:2107.11726 [nucl-th]

    work page arXiv 2021

  56. [56]

    Canonical and phenomenological formulations of spin hydrodynamics,

    A. Daher, A. Das, W. Florkowski, and R. Ryblewski, “Canonical and phenomenological formulations of spin hydrodynamics,” Phys. Rev. C 108 no. 2, (2023) 024902 , arXiv:2202.12609 [nucl-th]

    work page arXiv 2023

  57. [57]

    Sarwar, M

    G. Sarwar, M. Hasanujjaman, J. R. Bhatt, H. Mishra, and J.-e. Alam, “Causality and stability of relativistic spin hydrodynamics,” Phys. Rev. D 107 no. 5, (2023) 054031 , arXiv:2209.08652 [nucl-th]

    work page arXiv 2023

  58. [58]

    Stability studies of first-order spin-hydrodynamic frameworks,

    A. Daher, A. Das, and R. Ryblewski, “Stability studies of first-order spin-hydrodynamic frameworks,” Phys. Rev. D 107 no. 5, (2023) 054043 , arXiv:2209.10460 [nucl-th]

    work page arXiv 2023

  59. [59]

    Boost invariant spin hydrodynamics within the first order in derivative expansion,

    R. Biswas, A. Daher, A. Das, W. Florkowski, and R. Ryblewski, “Boost invariant spin hydrodynamics within the first order in derivative expansion,” Phys. Rev. D 107 no. 9, (2023) 094022 , arXiv:2211.02934 [nucl-th]

    work page arXiv 2023

  60. [60]

    Drogosz, W

    Z. Drogosz, W. Florkowski, N. /suppress Lygan, and R. Ryblewski, “Boost-invariant spin hydrodynamics with spin feedback effects,” Phys. Rev. C 111 no. 2, (2025) 024909 , arXiv:2411.06154 [hep-ph]

    work page arXiv 2025

  61. [61]

    Florkowski, Phenomenology of Ultra-Relativistic Heavy-Ion Collisions

    W. Florkowski, Phenomenology of Ultra-Relativistic Heavy-Ion Collisions . 2010

    2010

  62. [62]

    Vogt, Ultrarelativistic heavy-ion collisions

    R. Vogt, Ultrarelativistic heavy-ion collisions . Elsevier, Amsterdam, 2007

    2007

  63. [63]

    Electromagnetic probes of quark gluon plasma,

    J. Alam, B. Sinha, and S. Raha, “Electromagnetic probes of quark gluon plasma,” Phys. Rept. 273 (1996) 243–362

    1996

  64. [64]

    First-order relativistic hydrodynamics is stable,

    P. Kovtun, “First-order relativistic hydrodynamics i s stable,” JHEP 10 (2019) 034 , arXiv:1907.08191 [hep-th] . 17

    work page arXiv 2019

  65. [65]

    Relativistic second-order spin hydrodynamics: An entropy-current analysis,

    R. Biswas, A. Daher, A. Das, W. Florkowski, and R. Ryblewski, “Relativistic second-order spin hydrodynamics: An entropy-current analysis,” Phys. Rev. D 108 no. 1, (2023) 014024 , arXiv:2304.01009 [nucl-th]

    work page arXiv 2023

  66. [66]

    Rindori,Entropy current in relativistic quantum statistical mechanics

    D. Rindori, Entropy current in relativistic quantum statistical mechanics. PhD thesis, U. Florence (main), Florence U., 2020. arXiv:2110.07662 [hep-th]

    work page arXiv 2020

  67. [67]

    Coleman, Lectures of Sidney Coleman on Quantum Field Theory

    S. Coleman, Lectures of Sidney Coleman on Quantum Field Theory . WSP, Hackensack, 12, 2018

    2018

  68. [68]

    On the energy tensor of spinning massive matter in classical field theory and general relativity,

    F. W. Hehl, “On the energy tensor of spinning massive matter in classical field theory and general relativity,” Reports on Mathematical Physics 9 no. 1, (1976) 55–82

    1976

  69. [69]

    Spin tensor and pseudo-gauges: from nuclear collisions to gravitational physics,

    E. Speranza and N. Weickgenannt, “Spin tensor and pseudo-gauges: from nuclear collisions to gravitational physics,” Eur. Phys. J. A 57 no. 5, (2021) 155 , arXiv:2007.00138 [nucl-th]

    work page arXiv 2021

  70. [70]

    On the spin angular momentum of mesons,

    F. Belinfante, “On the spin angular momentum of mesons,” Physica 6 no. 7, (1939) 887–898

    1939

  71. [71]

    On the current and the density of the electric charge, the energy, the linear momentum and the angular momentum of arbitrary fields,

    F. Belinfante, “On the current and the density of the electric charge, the energy, the linear momentum and the angular momentum of arbitrary fields,” Physica 7 no. 5, (1940) 449–474

    1940

  72. [72]

    Rosenfeld Mem

    L. Rosenfeld Mem. Acad. Roy. Bel. 18 no. 1, (1940)

    1940

  73. [73]

    S. R. De Groot, W. A. Van Leeuwen, and C. G. Van Weert, Relativistic Kinetic Theory. Principles and Applications. North-Holland Publishing Company, 1980

    1980

  74. [74]

    On the spin angular momentum of the dirac particle,

    J. Hilgevoord and S. Wouthuysen, “On the spin angular momentum of the dirac particle,” Nuclear Physics 40 (1963) 1 – 12

    1963

  75. [75]

    The covariant definition of spin in relativistic quantum field theory,

    J. Hilgevoord and E. De Kerf, “The covariant definition of spin in relativistic quantum field theory,” Physica 31 no. 7, (1965) 1002–1016

    1965

  76. [76]

    Relativistic dynamics of spin-fluids and spin-particles,

    J. Weyssenhoff and A. Raabe, “Relativistic dynamics of spin-fluids and spin-particles,” Acta Phys. Polon. 9 (1947) 7–18

    1947

  77. [77]

    Highly Relativistic Nucleus-Nucleus Collisions: The Central Rapidity Region,

    J. D. Bjorken, “Highly Relativistic Nucleus-Nucleus Collisions: The Central Rapidity Region,” Phys. Rev. D27 (1983) 140–151

    1983

  78. [78]

    Reif, Fundamentals of Statistical and Thermal Physics

    F. Reif, Fundamentals of Statistical and Thermal Physics. 1965

    1965

  79. [79]

    Markoff Random Processes and the Statistical Mechanics of Time-Dependent Phenomena. II. Irreversible Processes in Fluids,

    M. S. Green, “Markoff Random Processes and the Statistical Mechanics of Time-Dependent Phenomena. II. Irreversible Processes in Fluids,” J. Chem. Phys. 22 (1954) 398

    1954

  80. [80]

    Statistical mechanical theory of irreversib le processes. 1. General theory and simple applications in magnetic and conduction problems,

    R. Kubo, “Statistical mechanical theory of irreversib le processes. 1. General theory and simple applications in magnetic and conduction problems,” J. Phys. Soc. Jap. 12 (1957) 570–586

    1957

Showing first 80 references.