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

By using the Tsallis Blast-Wave (TBW) model, we evaluate the transverse momentum spectra of protons and deuterons emitted in p-[Formula: see text] collisions at [Formula: see text] [Formula: see text]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 (q), the transverse flow velocity ([Formula: see text]), and the kinetic freeze-out temperature ([Formula: see text]). The system exhibits larger deviations from equilibrium (higher q), 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 q that are near to unity. These outcomes constrain the equation of state, exposing soft (hadronic) and stiff (QGP) behaviors across different multiplicities.