  We collected the transverse momentum (mass) spectra of charged hadrons
($\pi^{-}$, $\pi^{+}$, $K^{-}$, $K^{+}$, $\overline{p}$, and $p$) produced in
collisions over a center-of-mass energy range from 2.70 to 200 GeV (per nucleon
pair). The modified Tsallis--Pareto-type function (the TP-like function) with
average transverse flow velocity is used to describe the contribution of
participant or constituent quarks to transverse momentum of considered hadron.
The experimental spectra of $\pi^{\mp}$ and $K^{\mp}$ (or $\overline{p}$ and
$p$) are fitted by the convolution of two (or three) TP-like functions due to
the fact that two (or three) constituent quarks are regarded as two (or three)
energy resources in the formation of considered hadron. From the reasonable
fits to the spectra, the thermal freeze-out parameters are extracted, and the
pseudo-entropy is newly defined and extracted. Some parameters quickly change
in the energy range of less than 7.7 GeV, and slowly change in the energy range
of greater than 7.7 GeV, indicating the variation of collision mechanism at
around 7.7 GeV.
