Extracting the Speed of Sound in Heavy-Ion Collisions: A Study of Quantum-Initiated Fluctuations and Thermalization

The thermalization of quark-gluon plasma created in heavy-ion collisions is crucial for understanding its behavior as a relativistic fluid and the thermodynamic properties of the quantum chromodynamics (QCD). This study investigates the role of fluctuations in the relationship between transverse momentum and particle multiplicity, with a particular focus on their impact on extracting the QCD speed of sound. In a thermalized quark-gluon plasma, these fluctuations mostly originate from quantum fluctuations in the colliding nuclei, and exhibit a Gaussian distribution as a consequence of their independence from thermodynamic response. In contrast, nonthermalized systems display non-Gaussian fluctuations, reflecting the breakdown of thermalization. By leveraging the Gaussianity condition of quantum-initiated fluctuations, the physical value of the speed of sound can be extracted statistically, even in the presence of significant event-by-event fluctuations. This framework provides a robust diagnostic tool for probing thermalization and extracting thermodynamic properties in both large and small collision systems.