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To study the energy-dependent characteristics of thermodynamic andhydrodynamic parameters, based on the framework of a multi-source thermalmodel, we analyze the soft transverse momentum ($p_{T}$) spectra of the chargedparticles ($\pi^{-}$, $\pi^{+}$, $K^{-}$, $K^{+}$, $\bar{p}$, and $p$) producedin gold-gold (Au-Au) collisions at the center-of-mass energies$\sqrt{s_{NN}}=7.7$, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200 GeV from the STARCollaboration and in lead-lead (Pb-Pb) collisions at $\sqrt{s_{NN}}=2.76$ and5.02 TeV from the ALICE Collaboration. In the rest framework of emissionsource, the probability density function obeyed by meson momenta satisfies theBose-Einstein distribution, and that obeyed by baryon momenta satisfies theFermi-Dirac distribution. To simulate the $p_{T}$ of the charged particles, thekinetic freeze-out temperature $T$ and transverse expansion velocity$\beta_{T}$ of emission source are introduced into the relativistic ideal gasmodel. Our results, based on the Monte Carlo method for numerical calculation,show a good agreement with the experimental data. The excitation functions ofthermodynamic parameter $T$ and hydrodynamic parameter $\beta_{T}$ are thenobtained from the analyses, which shows an increase tendency from 7.7 GeV to5.02 TeV in collisions with different centralities.

Thermodynamic and hydrodynamic characteristics of interacting system formed in relativistic heavy ion collisions