Study of excitation function of p and d in different multiplicity events in p - Pb collisions at 8.16 TeV

Using the Tsallis Blast-Wave (TBW) model, we evaluate the transverse momentum spectra of protons and deuterons emitted in p-Pb collisions at [Formula: see text]=8.16 TeV in different multiplicity classes. Two distinctive dynamical regimes are distinguished by looking at the multiplicity reliance on key parameters, including the non-extensive parameter ([Formula: see text]), the transverse flow velocity ([Formula: see text]), and the kinetic freeze-out temperature ([Formula: see text]). The system exhibits larger deviations from equilibrium (higher [Formula: see text]), a lower [Formula: see text], and stronger collective flow in high-multiplicity collisions, which are a hallmark of a prolonged, QGP-like phase. Low-multiplicity events, on the other hand, exhibit a gradual shift toward thermal equilibrium with weaker flow, a higher [Formula: see text], and values of [Formula: see text] that are near to unity. These outcomes constrain the equation of state, exposing soft (hadronic) and stiff (QGP) behaviors across different multiplicities.