Enthalpy-Based Thermal Response and Its Exact Relation to the Speed of Sound in Finite-Temperature QCD

Abstract

A precise characterization of the QCD phase transition remains a fundamental open problem, primarily due to the intrinsically non-perturbative nature of the dynamics that govern the breakdown of We quantify the logarithmic thermal variation of the normalized enthalpy density in finite-temperature Quantum Chromodynamics using a dimensionless response thermal function, $\mathcal{H}(T)$. We establish an exact identity that links $\mathcal{H}(T)$ to the speed of sound, $c_s^2(T)$. Using continuum-extrapolated lattice Quantum Chromodynamics, Monte Carlo uncertainty propagation, and cubic spline interpolation, we extract a stable peak at $T_{\text{peak}}\approx 153.6\text{ MeV}$ (${\mathcal{H}}_{\text{peak}}\approx 6.24$), which remains robust under changes in the smoothing parameter $s$. By contrast, $\mathcal{H}(T)=0$ for the MIT Bag Model despite its non-vanishing trace anomaly. We highlight $\mathcal{H}(T)$ as an effective diagnostic of the QCD crossover and discuss its limitations for universal critical scaling at zero chemical potential.

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