Towards compressed baryonic matter densities: thermodynamics and transport coefficients

TL;DR

This work systematically compares three effective descriptions of hot and dense QCD matter—HRG, NJL, and a two-flavor chiral model—to map thermodynamic quantities and transport coefficients at finite baryon density. Using kinetic theory with the Boltzmann equation in the relaxation-time approximation and medium-dependent masses, it reveals that the Wiedemann–Franz law is strongly violated at low $\mu_B$ but gradually restored at higher density, while the shear-viscosity to entropy-density ratio $\eta/s$ stays nearly constant at small $\mu_B$ and increases with density. The results at finite density show convergence toward the massless (degenerate) limit in NJL and chiral models, with HRG deviating due to hadronic degrees of freedom, and draw qualitative parallels to graphene's Dirac/electron–hole plasma. The study provides a coherent, model-based framework for interpreting forthcoming CBM/NICA data and highlights potential fluid-to-nonfluid transitions in baryon-rich QCD matter.

Abstract

We study the thermodynamic and transport properties of hot and dense quantum chromodynamic matter expected to be produced in low-energy heavy-ion collisions, using three different effective quantum chromodynamic frameworks: the Nambu--Jona-Lasinio model, the chiral effective model, and the hadron resonance gas model. We briefly outline the theoretical formulation of thermodynamic quantities and transport coefficients within these approaches, where quarks are treated with effective masses in the Nambu--Jona-Lasinio and chiral effective models, and hadronic degrees of freedom are employed in the hadron resonance gas model. The transport coefficients are evaluated using the Boltzmann transport equation in the relaxation-time approximation. Following the theoretical overview, we present a comprehensive analysis of the behavior of these quantities as functions of the baryon chemical potential or net baryon density. The Lorenz ratio $κ/(σT)$ is found to increase rapidly-indicating a strong violation of the Wiedemann-Franz law in the low-$μ_{B}$ regime--while approaching the universal value at higher baryon chemical potentials or densities. The shear-viscosity-to-entropy-density ratio $η/s$ remains nearly constant at low $μ_{B}$ but exhibits a gradual increase as $μ_{B}$ grows. We also discuss the qualitative similarities of these trends with those observed in the electron-hole plasma of graphene, an emergent quasi-relativistic system characterized by massless energy-momentum dispersion.

Figures (8)

• Figure 1: (Color online) Top: normalized pressure $P/T^4$ and energy density $\varepsilon/T^4$ vs. $T$. Middle: total number density $n/T^3$ and entropy density $s/T^3$ vs. $T$. Bottom: dimensionless ratios $P/(nT)$ and $\varepsilon/(nT)$ vs. $T$. Results from the HRG, NJL, and chiral effective models are compared with the massless two-flavor quark limit.
• Figure 2: (Color online) Normalized electrical conductivity $\sigma/(\tau_c T^2)$ and shear viscosity $\eta/(\tau_c T^4)$ vs. $T$ in the HRG, NJL, and chiral effective models, compared with the corresponding massless two-flavor quark results.
• Figure 3: (Color online) Top: normalized pressure $P/\mu_B^4$ and energy density $\varepsilon/\mu_B^4$ vs. $n_{B}/n_{0}$. Middle: entropy density $s/\mu_B^3$ and enthalpy per baryon number $h/\mu_B$ vs. $n_B/n_0$. Bottom: dimensionless ratios $P/nT$ and $\varepsilon/nT$ vs. $n_B/n_0$. Results from the HRG, NJL, and chiral effective models are compared with the massless two-flavor quark limit.
• Figure 4: (Color online) Normalized electrical conductivity $\sigma/(\tau_c\mu_B^2)$, thermal conductivity $\kappa/(\tau_c\mu_B^3)$ and shear viscosity $\eta/(\tau_c\mu_B^4)$ as a function of scaled baryon density $n_B/n_0$ in HRG, NJL and chiral effective models compared with the corresponding values for a massless two-flavor quark system. The dimensionless ratio $\kappa/(\sigma T)$ is also plotted for all the cases.
• Figure 5: (Color online) Shear viscosity to entropy density ratio $\eta/s$ as a function of $\mu_B/T$ in HRG, NJL, and chiral effective models compared with the corresponding values for a massless two-flavor quark system. A constant relaxation time of 1.25 fm is assumed throughout the entire density range.