- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review C

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Nonlinear analysis of causality for heat flow in heavy-ion collisions: Constraints from the equation of state

Victor Roy*

  • *Contact author: victor@niser.ac.in
PDF

Phys. Rev. C 113, 034913 – Published 17 March, 2026

DOI: https://doi.org/10.1103/ftyb-dps7

Abstract

The present work investigates the causal parameter space of the Mueller-Israel-Stewart second-order theory for heat-conducting fluids in the Eckart frame for one-dimensional fluid flow in systems with finite baryon density. It is shown that this parameter space is highly constrained and particularly sensitive to the equation of state and second-order transport coefficients. Through numerical analysis of the characteristic equations, the present analysis identifies regions of strong hyperbolicity, weak hyperbolicity, and nonhyperbolicity, mapping the boundaries of causality violation as functions of the heat flux to energy density ratio q/ɛ and relaxation parameters. The present work also explores the causality conditions using a realistic lattice QCD based equation of state. Using the Navier-Stokes approximation, an estimate is made of the heat flow magnitude to assess causality criteria for one-dimensional heat conduction in heavy-ion collisions. The present calculations reveal unrealistically large heat flux values (|q|/ɛ≈330–811) for typical conditions at the BNL Relativistic Heavy Ion Collider when using thermal conductivity estimates from kinetic theory models, suggesting either significant overestimation of transport coefficients or breakdown of the fluid approximation in these extreme conditions. The pressure gradient corrections reduce the heat flow by approximately 15% but do not resolve the causality concerns.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (48)

  1. W. Israel, Nonstationary irreversible thermodynamics: A causal relativistic theory, Ann. Phys. 100, 310 (1976).
  2. W. Israel and J. M. Stewart, Transient relativistic thermodynamics and kinetic theory, Ann. Phys. 118, 341 (1979).
  3. L. Landau and E. Lifshitz, Fluid Mechanics (Pergamon, Oxford, 1987).
  4. C. Eckart, The thermodynamics of irreversible processes. III. Relativistic theory of the simple fluid, Phys. Rev. 58, 919 (1940).
  5. G. S. Denicol, H. Niemi, E. Molnar, and D. H. Rischke, Derivation of transient relativistic fluid dynamics from the Boltzmann equation, Phys. Rev. D 85, 114047 (2012).
  6. R. Baier, P. Romatschke, D. T. Son, A. O. Starinets, and M. A. Stephanov, Relativistic viscous hydrodynamics, conformal invariance, and holography, J. High Energy Phys. 04 (2008) 100.
  7. M. Bemfica, M. M. Disconzi, J. Noronha, and P. Kovtun, Nonlinear causality of general first-order relativistic viscous hydrodynamics, Phys. Rev. D 100, 104020 (2019).
  8. A. Pandya, E. R. Most, and F. Pretorius, Causal, stable first-order viscous relativistic hydrodynamics with ideal gas microphysics, Phys. Rev. D 106, 123036 (2022).
  9. F. S. Bemfica, M. M. Disconzi, and J. Noronha, First-order general-relativistic viscous fluid dynamics, Phys. Rev. X 12, 021044 (2022).
  10. D. Jou, J. Casas-Vázquez, and G. Lebon, Extended Irreversible Thermodynamics (Springer, Berlin, 1996).
  11. L. Rezzolla and O. Zanotti, Relativistic Hydrodynamics (Oxford University Press, Oxford, 2013).
  12. Y. Aharonov, A. Komar, and L. Susskind, Superluminal behavior, causality, and instability, Phys. Rev. 182, 1400 (1969).
  13. E. Krotscheck and W. Kundt, Causality criteria, Commun. Math. Phys. 60, 171 (1978).
  14. L. Gavassino, M. Antonelli, and B. Haskell, When the entropy has no maximum: A new perspective on the instability of the first-order theories of dissipation, Phys. Rev. D 102, 043018 (2020).
  15. L. Gavassino, Causality constraints on radiative transfer, Phys. Rev. D 111, 103011 (2025).
  16. S. Floerchinger, F. C. Grossi, Causality of fluid dynamics for high-energy nuclear collisions, J. High Energy Phys. 08 (2018) 186.
  17. S. Pu, T. Koide, and D. H. Rischke, Does stability of relativistic dissipative fluid dynamics imply causality? Phys. Rev. D 81, 114039 (2010).
  18. R. Biswas, S. Mitra, and V. Roy, An expedition to the islands of stability in the first-order causal hydrodynamics, Phys. Lett. B 838, 137725 (2023)
  19. R. Biswas, A. Dash, N. Haque, S. Pu, and V. Roy, Causality and stability in relativistic viscous non-resistive magneto-fluid dynamics, J. High Energy Phys. 10 (2020) 171.
  20. J. Sammet, M. Mayer, and D. H. Rischke, Linear stability analysis of Israel-Stewart theory in the case of a nonzero background charge, Phys. Rev. D 107, 114028 (2023)).
  21. S. Bhattacharyya, S. Mitra, and S. Roy, Causality and stability in relativistic hydrodynamic theory - a choice to be endured, Phys. Lett. B 856, 138918 (2024).
  22. M. Spaliński and B. Withers, Causality and classical dispersion relations, Phys. Rev. D 109, 046018 (2024).
  23. G. Perna and E. Calzetta, Linearized dispersion relations in viscous relativistic hydrodynamics, Phys. Rev. D 104, 096005 (2021).
  24. C. V. Brito and G. S. Denicol, Linear causality and stability of third-order relativistic dissipative fluid dynamics, Phys. Rev. D 105, 096026 (2022).
  25. F. S. Bemfica, M. M. Disconzi, and J. Noronha, Causality of the Einstein-Israel-Stewart theory with bulk viscosity, Phys. Rev. Lett. 122, 221602 (2019).
  26. D.-L. Wang and S. Pu, Stability and causality criteria in linear mode analysis: Stability means causality, Phys. Rev. D 109, L031504 (2024).
  27. W. A. Hiscock and L. Lindblom, Generic instabilities in first-order dissipative relativistic fluid theories, Phys. Rev. D 31, 725 (1985).
  28. P. Romatschke, New developments in relativistic viscous hydrodynamics, Int. J. Mod. Phys. E 19, 1 (2010).
  29. T. Hoshino and T. Hirano, Constraint on initial conditions of one-dimensional expanding fluids from nonlinear causality, Phys. Rev. C 111, 014913 (2025).
  30. I. Cordeiro, F. S. Bemfica, E. Speranza, and J. Noronha, Nonlinear causality of Israel-Stewart theory with diffusion, Phys. Rev. D 113, 045024 (2026).
  31. I. Cordeiro, et al., Causality bounds on dissipative general-relativistic magnetohydrodynamics, Phys. Rev. Lett. 133, 091401 (2024)),
  32. L. Gavassino, Relativistic heat conduction in the large-flux regime, Entropy 26, 147 (2024).
  33. W. A. Hiscock and L. Lindblom, Nonlinear pathologies in relativistic heat-conducting fluid theories, Phys. Lett. A 131, 509 (1988).
  34. P. Danielewicz and M. Gyulassy, Dissipative phenomena in quark-gluon plasmas, Phys. Rev. D 31, 53 (1985).
  35. T. Kunihiro and K. Tsumura, Stable first-order particle-frame relativistic hydrodynamics for dissipative systems, Phys. Lett. B 668, 425 (2008).
  36. A. Monnai, Landau and Eckart frames for relativistic fluids in nuclear collisions, Phys. Rev. C 100, 014901 (2019)
  37. J. I. Kapusta and C. Gale, Finite-Temperature Field Theory: Principles and Applications, 2nd ed. (Cambridge University Press, Cambridge, 2006).
  38. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (John Wiley & Sons, New York, 1972).
  39. P. F. Bedaque and A. W. Steiner, Sound velocity bound and neutron stars, Phys. Rev. Lett. 114, 031103 (2015).
  40. S. Borsányi, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, and K. K. Szabó, Full result for the QCD equation of state with 2+1 flavors, Phys. Lett. B 730, 99 (2014)).
  41. S. Chakrabarty, Transport coefficients of quark-gluon plasma, Pramana 25, 673 (1985).
  42. S. Mitra and V. Chandra, Transport coefficients of a hot QCD medium and their relative significance in heavy-ion collisions, Phys. Rev. D 96, 094003 (2017)
  43. G. Kadam, H. Mishra, and L. Thakur, Electrical and thermal conductivities of hot and dense hadronic matter, Phys. Rev. D 98, 114001 (2018).
  44. M. Greif, F. Reining, I. Bouras, G. S. Denicol, Z. Xu, and C. Greiner, Heat conductivity in relativistic systems investigated using a partonic cascade, Phys. Rev. E 87, 033019 (2013)
  45. R. Marty, E. Bratkovskaya, W. Cassing, J. Aichelin, and H. Berrehrah, Transport coefficients from the Nambu–Jona-Lasinio model for SU(3) f, Phys. Rev. C 88, 045204 (2013)
  46. S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge, 1973).
  47. W. A. Hiscock and T. S. Olson, Effects of frame choice on nonlinear dynamics in relativistic heat-conducting fluid theories, Phys. Lett. A 141, 125 (1989).
  48. C. Plumberg, et al., Causality violations in realistic simulations of heavy-ion collisions, Phys. Rev. C 105, L061901 (2022).

Outline

Information

Phys. Rev. C 113, 034913– Published 17 March, 2026
  • Received 3 November 2025
  • Revised 21 January 2026
  • Accepted 20 February 2026
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation