Causal Theories of Dissipative Relativistic Fluid Dynamics for Nuclear Collisions

TL;DR

This paper argues that relativistic dissipative fluid dynamics in ultra-relativistic nuclear collisions requires hyperbolic, second-order (Müller–Israel–Stewart) formalisms to preserve causality and stability, especially at early times. It contrasts first-order Navier–Stokes–Fourier theories with second-order Israel–Stewart dynamics, showing that the latter better reproduce transport-model behavior and predict more physical evolution in Bjorken-like expansion. By applying these frameworks to both partonic (quark–gluon plasma) and hadronic (pion gas) regimes, the work demonstrates improved consistency with kinetic descriptions and highlights the importance of relaxation times and new transport coefficients. The study emphasizes the need for realistic equations of state, quantitative transport coefficients, and full 3D numerical implementations to connect theory with observables at RHIC and LHC.

Abstract

Non-equilibrium fluid dynamics derived from the extended irreversible thermodynamics of the causal Müller--Israel--Stewart theory of dissipative processes in relativistic fluids based on Grad's moment method is applied to the study of the dynamics of hot matter produced in ultra--relativistic heavy ion collisions. The temperature, energy density and entropy evolution are investigated in the framework of the Bjorken boost--invariant scaling limit. The results of these second order theories are compared to those of first order theories due to Eckart and to Landau and Lifshitz and those of zeroth order (perfect fluid) due to Euler. In the presence of dissipation perfect fluid dynamics is no longer valid in describing the evolution of the matter. First order theories fail in the early stages of evolution. Second order theories give a better description in good agreement with transport models. It is shown in which region the Navier--Stokes--Fourier laws (first order theories) are a reasonable limiting case of the more general extended thermodynamics (second order theories).

Figures (14)

• Figure 1: The transverse ($v_T$), longitudinal ($v_L$) and sound ($v_s$) phase velocities in a pion gas, as a function of $z=m/T$. $m$ is the mass of pion.
• Figure 2: The transverse ($v_T$), longitudinal ($v_1,\,v_2$) and sound ($v_s$) phase velocities in a nucleon gas, as a function of $z=m/T$. $m$ is the mass of nucleon.
• Figure 3: Proper time evolution for temperature, energy density and entropy density in the Bjorken model for nuclear collisions (longitudinal expansion only).
• Figure 4: The $\tau$ dependence of temperature $T$, entropy density $s$ and the inverse of Reynolds number $R^{-1}$ in the scaling solution with $s$ and $\eta$ are proportional to $T^3$.
• Figure 5: The $\alpha_s$ dependence of $R_0$ and the region which satisfies $R_0\geq1$ is shown in the $\alpha_s$--$T_0\tau_0$ plane; where the curve is the condition $R_0=1$.