  We examined the transverse momentum spectra of various identified particles,
across different multiplicity classes in proton-proton collisions at a
center-of-mass energy of $\sqrt{s}$ = 7 TeV. Utilizing the Tsallis and Hagedorn
models, parameters relevant to the bulk properties of nuclear matter were
extracted. Both models exhibit good agreement with experimental data. In our
analyses, we observed a consistent decrease in the effective temperature for
the Tsallis model and the kinetic or thermal freeze-out temperature for the
Hagedorn model, as we transition from higher multiplicity (class-I) to lower
multiplicity (class-X). Additionally, the transverse flow velocity experiences
a decline from class-I to class-X. The normalization constant which represents
the multiplicity of produced particles is observed to decrease as we move
towards higher multiplicity classes. While the effective and kinetic freeze-out
temperatures, as well as the transverse flow velocity, show a mild dependency
on multiplicity for lighter particles, this relationship becomes more
pronounced for heavier particles. Various particle species are observed to
undergo decoupling from the fireball at distinct temperatures: lighter
particles exhibit lower temperatures, while heavier ones show higher
temperatures, thereby supporting the concept of multiple freeze-out scenarios.
Moreover, we identified a positive correlation between the kinetic freeze-out
temperature and transverse flow velocity, a scenario where particles experience
stronger collective motion at higher freeze-out temperature. The reason for
this positive correlation is that as the multiplicity increases, more energy is
transferred into the system. This heightened energy causes greater excitation
and pressure within the system, leading to a quick expansion.
