Kinetic-Theory Bounds on the Equation of State of Dense QCD Matter

TL;DR

The paper addresses how to bound the equation of state (EOS) of cold, dense QCD matter by extending a model-agnostic χEFT–pQCD interpolation with a microscopic kinetic-theory (KT) constraint. It combines causality and thermodynamic stability bounds with an additional KT bound on the speed of sound, activated above an onset density $n_{\rm th}$, to produce a density-dependent tightening of the admissible EOS band. A key result is that the KT constraint substantially reduces the high-density region of the EOS space, with the extent controlled by $n_{\rm th}$ and the pQCD scale parameter $X$, while the low-density bound remains largely unchanged. This provides a physically motivated prior that connects microscopic transport stability to astrophysical EOS inferences, potentially improving neutron-star phenomenology and EOS inference under realistic transport assumptions.

Abstract

We derive bounds on the equation of state of cold, dense matter by extending the causal, model-agnostic interpolation between chiral effective field theory and perturbative calculations with a microscopic constraint from relativistic kinetic theory. The additional condition restricts the stiffest admissible behavior of the equation of state and systematically reduces the range of allowed equations of state, with the strongest effect at high densities. The resulting bounds remain consistent with known low- and high-density limits, while the strength of the constraint depends on the density above which the kinetic-theory condition is applied. These bounds can be readily incorporated into future studies of cold, dense matter and used to assess the impact of microscopic stability conditions on equation-of-state inference.

Figures (5)

• Figure 1: Bounds on the baryon density, $n(\mu)$, as a function of baryon chemical potential $\mu$, for the ${\rm pQCD}$ scale parameter $X=2$. Solid, blue lines represent bounds from causality, i.e., $c_s^2 \leq 1$. Dashed, blue lines show the integral constraints (see Section \ref{['sec:causal']} for details). Solid and dashed red lines show bounds from kinetic theory and kinetic theory combined with integral constraint, respectively (see Section \ref{['sec:kt']} for details). We note that the integral constraints are not shown outside of the regions already constrained by either bounds. The gray dots mark the theoretical constraints from ${\chi \rm EFT}$ at low density and pQCD at high density. The gray, dotted vertical line marks the density threshold $n_{\rm th}$ above which the kinetic theory constraint is applied. Here, as an example, $n_{\rm th}=20\,n_{\rm sat}$ was used. Note that the lower causal and kinetic theory bounds overlap in this example.
• Figure 2: The construction of the density $n_{\rm min}(\mu)$ that maximizes the thermodynamic pressure at $\mu > \mu_x$ (top panel) and density $n_{\rm max}(\mu)$ that minimize the thermodynamic pressure at $\mu < \mu_x$ (bottom panel). Note that the functions $n_{\rm min}(\mu)$ and $n_{\rm max}(\mu)$ are extrapolated from $(\mu_L,n_L)$ and $(\mu_H, n_H)$, respectively.
• Figure 3: The construction of the density that includes the kinetic theory constraint at $n > n_{\rm th}$ (or equivalently at $\mu > \mu_{\rm th}$). The density $n^{\rm KT}_{\rm min}$ (panels a and b) maximizes the thermodynamic pressure at $\mu > \mu_x$ and $n^{\rm KT}_{\rm max}$ (panels c and a) minimizes the thermodynamic pressure $\mu < \mu_x$. The construction of the densities depends whether $\mu_{\rm th} > \mu_x$ (panels a and c) or $\mu_{\rm th} < \mu_x$ (panels b and d). The red triangles mark the onset of the kinetic theory ansatz. Note that the functions $n^{\rm KT}_{\rm min}$ and $n^{\rm KT}_{\rm max}$ are extrapolated from $(\mu_L,n_L)$ and $(\mu_H, n_H)$, respectively.
• Figure 4: Constraints on the thermodynamic pressure, $p$, as function of energy density, $\epsilon$, obtained by mapping the allowed $n(\mu)$ space for different values of $n_{\rm th}$ (see text for details). The gray circles mark the theoretical constraints from $\chi$EFT at low density and pQCD at high density.
• Figure 5: Fraction of the area excluded in the $p-\epsilon$ plane as a function of the onset density for the kinetic-theory constraint, $n_{\rm th}$, in the units of saturation density. The effect of varying the scale parameter $X \in [1, 4]$ is included in the orange band.