The thermodynamic quantities of the ideal gas of hadrons and the \((2+1)\)-flavor lattice QCD scaled by the effective degeneracy factors of the corresponding models are compared. We have found that in terms of the scaled variables the quark-hadron duality of the lattice QCD and the hadron resonance gas (HRG) model disappears. However, we have revealed that the scaled variables lead to the quark-hadron duality of the lattice QCD and the quantum ideal gas of kaons and antikaons, namely, the ideal gas of those hadrons that contain all the three quarks u, d, s and their antiquarks. Satisfactory agreement between the scaled results of the kaon ideal gas and the lattice QCD data is achieved at large values of the volume in the entire temperature range. In the ideal gas of kaons there is no any phase transition. Nevertheless, in our calculations the scaled thermodynamic quantities of the ideal gas and the lattice QCD follow the same qualitative behavior and are consistent with each other especially at high temperatures in the perturbative region and the Stefan–Boltzmann limit.

中文翻译：

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比例变量和夸克-强子对偶

比较了强子的理想气体的热力学量和由相应模型的有效简并因子定标的（（2 + 1）\）味晶格QCD的热力学量。我们已经发现，就比例变量而言，晶格QCD和强子共振气体（HRG）模型的夸克-强子对偶性消失了。然而，我们已经揭示了这些定标变量导致了晶格QCD的夸克-强子对偶性以及kaon和antikaons的量子理想气体，即包含所有三个夸克u，  d，  s的那些强子的理想气体。和他们的夸克。在整个温度范围内，在较大的体积值下，kaon理想气体的定标结果与晶格QCD数据之间达到了令人满意的一致性。在理想的钾离子气体中，没有任何相变。然而，在我们的计算中，理想气体和晶格QCD的比例热力学量遵循相同的定性行为，并且彼此一致，特别是在摄动区域和Stefan-Boltzmann极限的高温下。