Near-thermal state and thermodynamic response of a QCD system in ultra-central heavy-ion collisions

Abstract

We present a systematic framework to extract QCD thermodynamic properties at finite baryon density from ultra-central heavy-ion collisions, where the impact parameter is nearly zero and volume fluctuations are strongly suppressed. By mapping the measured multi-particle state of each event to an effective homogeneous fireball through the conservation of total energy, total entropy and net baryon number, a near-thermal state with variations is realized from event to event, which allows thermodynamic response relations to be tested. Using STAR Beam Energy Scan data on charged particle multiplicity and net proton fluctuations, we show that the thermalization condition is satisfied within uncertainties across collision energies, validating the interpretation of ultra-central events as small deviations from a thermally equilibrated state. We then generalize the response relations to finite baryon chemical potential, expressing the response coefficients in terms of the speed of sound and susceptibilities. Our results provide a baseline for using ultra-central collisions to probe the QCD equation of state and phase structure, including the search for the critical endpoint.