Percolation of color sources and the equation of state of QGP in central Au–Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV

The Color String Percolation Model (CSPM) is used to determine the equation of state (EOS) of the Quark–Gluon Plasma (QGP) produced in central Au–Au collisions at \(\sqrt{s_{\mathit{NN}}} = 200\) A GeV using STAR data at RHIC. When the initial density of interacting colored strings exceeds the 2D percolation threshold a cluster is formed, which defines the onset of color deconfinement. These interactions also produce fluctuations in the string tension which transforms the Schwinger particle (gluon) production mechanism into a maximum entropy thermal distribution analogous to QCD Hawking–Unruh radiation. The single string tension is determined by identifying the known value of the universal hadron limiting temperature T c =167.7±2.6 MeV with the CSPM temperature at the critical percolation threshold parameter ξ c =1.2. At midrapidity the initial Bjorken energy density and the initial temperature determine the number of degrees of freedom consistent with the formation of a ∼2+1 flavor QGP. An analytic expression for the equation of state, the sound velocity \(C_{s}^{2}(\xi)\) is obtained in CSPM. The CSPM \(C_{s}^{2}(\xi)\) and the bulk thermodynamic values energy density ε/T 4 and entropy density s/T 3 are in excellent agreement in the phase transition region with recent lattice QCD simulations (LQCD) by the HotQCD Collaboration.