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# The isentropic equation of state of (2+1)-flavor QCD: An update based on high precision Taylor expansion and Pad\'e-resummed expansion at finite chemical potentials

Dec 2022

The HotQCD Collaboration performed Taylor expansion calculations in 2017 forthe pressure, energy density, and entropy density at non-zero chemicalpotentials up to the $6^th$ order. Since then, they have significantly improvedthe statistics for lattices with temporal extents of $N_\tau=8$ and $12$, andhave also included results for $N_\tau=16$ that were not previously available.They have also calculated the $8^th$-order expansion coefficients for$N_\tau=8$. These calculations showed that the Taylor series expansion for thepressure is accurate up to $\mu_B / T \leq 2.5$. In this study, we use thehigh-statistics results on Taylor expansion coefficients, calculated with HISQfermions and extrapolated to the continuum limit, to determine the QCD equationof state under conditions relevant for hot and dense matter produced in heavyion collisions. We also calculate the energy density and pressure along linesof constant entropy per net baryon number.

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