Polyakov loop in 2+1 flavor QCD from low to high temperatures

We study the free energy of a static quark in QCD with 2+1 flavors in a wide temperature region, 116 MeV $< T <$ 5814 MeV, using the highly improved staggered quark (HISQ) action. We analyze the transition region in detail, obtain the entropy of a static quark, show that it peaks at temperatures close to the chiral crossover temperature and also revisit the temperature dependence of the Polyakov loop susceptibilities using gradient flow. We discuss the implications of our findings for the deconfinement and chiral crossover phenomena at physical values of the quark masses. Finally a comparison of the lattice results at high temperatures with the weak-coupling calculations is presented.