Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Application range of perfect spin hydrodynamics

Zbigniew Drogosz*, Wojciech Florkowski†, and Valeriya Mykhaylova‡

  • *Contact author: zbigniew.drogosz@alumni.uj.edu.pl
  • †Contact author: wojciech.florkowski@uj.edu.pl
  • ‡Contact author: valeriya.mykhaylova@uj.edu.pl

Phys. Rev. D 112, L051901 – Published 8 September, 2025

DOI: https://doi.org/10.1103/tg2w-czwq

Abstract

The application range of perfect spin hydrodynamics is studied in two cases: one based on the classical spin description and the other using a quantum spin density matrix (Wigner function). Different forms of the conditions connecting the components of the spin-polarization tensor, particle mass, temperature, and hydrodynamic flow are introduced, and their mutual relations are explained. The results obtained are important for practical applications of spin hydrodynamics to model heavy-ion collisions.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (62)

  1. Z.-T. Liang and X.-N. Wang, Globally polarized quark-gluon plasma in non-central A+A collisions, Phys. Rev. Lett. 94, 102301 (2005); 96, 039901(E) (2006).
  2. Z.-T. Liang and X.-N. Wang, Spin alignment of vector mesons in non-central A+A collisions, Phys. Lett. B 629, 20 (2005).
  3. L. Adamczyk et al. (STAR Collaboration), Global Λ hyperon polarization in nuclear collisions: Evidence for the most vortical fluid, Nature (London) 548, 62 (2017).
  4. J. Adam et al. (STAR Collaboration), Global polarization of Λ hyperons in Au+Au collisions at sNN=200  GeV, Phys. Rev. C 98, 014910 (2018).
  5. J. Adam et al. (STAR Collaboration), Polarization of Λ (Λ¯) hyperons along the beam direction in Au+Au collisions at sNN=200  GeV, Phys. Rev. Lett. 123, 132301 (2019).
  6. S. Acharya et al. (ALICE Collaboration), Evidence of spin-orbital angular momentum interactions in relativistic heavy-ion collisions, Phys. Rev. Lett. 125, 012301 (2020).
  7. T. Niida and S. A. Voloshin, Polarization phenomenon in heavy-ion collisions, Int. J. Mod. Phys. E 33, 2430010 (2024).
  8. F. Becattini and L. Tinti, The Ideal relativistic rotating gas as a perfect fluid with spin, Ann. Phys. (N.Y.) 325, 1566 (2010).
  9. F. Becattini, Hydrodynamics of fluids with spin, Phys. Part. Nucl. Lett. 8, 801 (2011).
  10. F. Becattini, V. Chandra, L. Del Zanna, and E. Grossi, Relativistic distribution function for particles with spin at local thermodynamical equilibrium, Ann. Phys. (N.Y.) 338, 32 (2013).
  11. D. Montenegro, L. Tinti, and G. Torrieri, Ideal relativistic fluid limit for a medium with polarization, Phys. Rev. D 96, 056012 (2017); 96, 079901(A) (2017).
  12. W. Florkowski, B. Friman, A. Jaiswal, and E. Speranza, Relativistic fluid dynamics with spin, Phys. Rev. C 97, 041901 (2018).
  13. 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. D 97, 116017 (2018).
  14. W. Florkowski, A. Kumar, and R. Ryblewski, Thermodynamic versus kinetic approach to polarization-vorticity coupling, Phys. Rev. C 98, 044906 (2018).
  15. 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. B 795, 100 (2019).
  16. 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, Phys. Rev. D 100, 056018 (2019).
  17. W. Florkowski, A. Kumar, R. Ryblewski, and R. Singh, Spin polarization evolution in a boost invariant hydrodynamical background, Phys. Rev. C 99, 044910 (2019).
  18. S. Bhadury, W. Florkowski, A. Jaiswal, A. Kumar, and R. Ryblewski, Relativistic dissipative spin dynamics in the relaxation time approximation, Phys. Lett. B 814, 136096 (2021).
  19. D. Montenegro and G. Torrieri, Linear response theory and effective action of relativistic hydrodynamics with spin, Phys. Rev. D 102, 036007 (2020).
  20. 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, 052301 (2021).
  21. S. Shi, C. Gale, and S. Jeon, From chiral kinetic theory to relativistic viscous spin hydrodynamics, Phys. Rev. C 103, 044906 (2021).
  22. S. Bhadury, W. Florkowski, A. Jaiswal, A. Kumar, and R. Ryblewski, Dissipative spin dynamics in relativistic matter, Phys. Rev. D 103, 014030 (2021).
  23. K. Fukushima and S. Pu, Spin hydrodynamics and symmetric energy-momentum tensors—A current induced by the spin vorticity–, Phys. Lett. B 817, 136346 (2021).
  24. S. Li, M. A. Stephanov, and H.-U. Yee, Nondissipative second-order transport, spin, and pseudogauge transformations in hydrodynamics, Phys. Rev. Lett. 127, 082302 (2021).
  25. R. Singh, G. Sophys, and R. Ryblewski, Spin polarization dynamics in the Gubser-expanding background, Phys. Rev. D 103, 074024 (2021).
  26. A. D. Gallegos, U. Gürsoy, and A. Yarom, Hydrodynamics of spin currents, SciPost Phys. 11, 041 (2021).
  27. N. Weickgenannt, E. Speranza, X.-l. Sheng, Q. Wang, and D. H. Rischke, Derivation of the nonlocal collision term in the relativistic Boltzmann equation for massive spin-1/2 particles from quantum field theory, Phys. Rev. D 104, 016022 (2021).
  28. D. She, A. Huang, D. Hou, and J. Liao, Relativistic viscous hydrodynamics with angular momentum, Sci. Bull. 67, 2265 (2022).
  29. M. Hongo, X.-G. Huang, M. Kaminski, M. Stephanov, and H.-U. Yee, Relativistic spin hydrodynamics with torsion and linear response theory for spin relaxation, J. High Energy Phys. 11 (2021) 150.
  30. J. Hu, Relativistic first-order spin hydrodynamics via the Chapman-Enskog expansion, Phys. Rev. D 105, 076009 (2022).
  31. R. Singh, M. Shokri, and S. M. A. T. Mehr, Relativistic hydrodynamics with spin in the presence of electromagnetic fields, Nucl. Phys. A 1035, 122656 (2023).
  32. 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, 096014 (2022).
  33. D. Wagner, N. Weickgenannt, and D. H. Rischke, Lorentz-covariant nonlocal collision term for spin-1/2 particles, Phys. Rev. D 106, 116021 (2022).
  34. S. Dey, W. Florkowski, A. Jaiswal, and R. Ryblewski, Pseudogauge freedom and the SO(3) algebra of spin operators, Phys. Lett. B 843, 137994 (2023).
  35. N. Weickgenannt and J.-P. Blaizot, Chiral hydrodynamics of expanding systems, Phys. Rev. D 109, 056012 (2024).
  36. A. Kumar, D.-L. Yang, and P. Gubler, Spin alignment of vector mesons by second-order hydrodynamic gradients, Phys. Rev. D 109, 054038 (2024).
  37. D. Wagner, M. Shokri, and D. H. Rischke, Damping of spin waves, Phys. Rev. Res. 6, 043103 (2024).
  38. D. Wagner, Resummed spin hydrodynamics from quantum kinetic theory, Phys. Rev. D 111, 016008 (2025).
  39. 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, 074037 (2025).
  40. D. She, Y.-W. Qiu, and D. Hou, Relativistic second-order spin hydrodynamics: A Kubo-type formulation for the quark-gluon plasma, Phys. Rev. D 111, 036027 (2025).
  41. X.-G. Huang, An introduction to relativistic spin hydrodynamics, Nuclear Science and Techniques 36, 208 (2025).
  42. S. Bhadury, Relativistic spin hydrodynamics from novel relaxation time approximation, Phys. Rev. C 112, L021901 (2025).
  43. S. Dey, Virial theorem for rigidly rotating matter, arXiv:2504.18388.
  44. N. Weickgenannt and J.-P. Blaizot, Spin kinetic theory with a nonlocal relaxation time approximation, Phys. Rev. D 111, 056006 (2025).
  45. J.-Y. Ollitrault, Relativistic hydrodynamics for heavy-ion collisions, Eur. J. Phys. 29, 275 (2008).
  46. P. Romatschke, New Developments in Relativistic Viscous Hydrodynamics, Int. J. Mod. Phys. E 19, 1 (2010).
  47. W. Florkowski, Phenomenology of Ultra-Relativistic Heavy-Ion Collisions (World Scientific, Singapore, 2010).
  48. C. Gale, S. Jeon, and B. Schenke, Hydrodynamic modeling of heavy-ion collisions, Int. J. Mod. Phys. A 28, 1340011 (2013).
  49. A. Jaiswal and V. Roy, Relativistic hydrodynamics in heavy-ion collisions: general aspects and recent developments, Adv. High Energy Phys. 2016, 9623034 (2016).
  50. S. K. Singh, R. Ryblewski, and W. Florkowski, Spin dynamics with realistic hydrodynamic background for relativistic heavy-ion collisions, Phys. Rev. C 111, 024907 (2025).
  51. Sapna, S. K. Singh, and D. Wagner, Spin polarization of Λ hyperons from dissipative spin hydrodynamics, arXiv:2503.22552.
  52. W. Florkowski, A. Kumar, and R. Ryblewski, Relativistic hydrodynamics for spin-polarized fluids, Prog. Part. Nucl. Phys. 108, 103709 (2019).
  53. W. Florkowski and M. Hontarenko, Generalized thermodynamic relations for perfect spin hydrodynamics, Phys. Rev. Lett. 134, 082302 (2025).
  54. Z. Drogosz, W. Florkowski, and M. Hontarenko, Hybrid approach to perfect and dissipative spin hydrodynamics, Phys. Rev. D 110, 096018 (2024).
  55. S. Bhadury, Z. Drogosz, W. Florkowski, S. K. Kar, and V. Mykhaylova, Local equilibrium Wigner function for spin-1/2 particles, arXiv:2505.02657.
  56. M. Mathisson, Neue mechanik materieller systemes, Acta Phys. Pol. 6, 163 (1937).
  57. M. Mathisson, Republication of: New mechanics of material systems, Gen. Relativ. Gravit. 42, 1011 (2010).
  58. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1998).
  59. R. Singh (private communication), see also https://indico.cern.ch/event/1334113/contributions/6291310/attachments/3044936/5379962/QM2025_Abboud_Poster.pdf.
  60. N. Abboud, L. Gavassino, R. Singh, and E. Speranza, The perfect spinfluid, arXiv:2506.19786.
  61. J. Frenkel, Die elektrodynamik des rotierenden elektrons, Z. Phys. 37, 243 (1926).
  62. Z. Drogosz, Hybrid framework of Fermi-Dirac spin hydrodynamics, Physics 7, 31 (2025).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation