  We describe the transverse momentum (or mass) spectra of $\pi^\pm$, $K^\pm$,
$p$, and $\bar{p}$ produced in central gold-gold (Au-Au), central lead-lead
(Pb-Pb), and inelastic proton-proton ($pp$) collisions at different collision
energies range from the AGS to LHC by using a two-component (in most cases)
Erlang distribution in the framework of multi-source thermal model. The fitting
results are consistent with the experimental data and the energy-dependent
chemical potentials of light hadrons ($\pi$, $K$, and $p$) and quarks ($u$,
$d$, and $s$) in central Au-Au, central Pb-Pb, and inelastic $pp$ collisions
from the yield ratios of negative to positive particles obtained from the
normalization constants are then extracted. The study shows that most types of
energy-dependent chemical potentials decrease with increase of collision energy
over a range from the AGS to LHC. The curves of all types of energy-dependent
chemical potentials, obtained from the linear fits of yield ratios vs energy,
have inflection points at the same energy of 3.526 GeV, which is regarded as
the critical energy of phase transition from a hadron liquid-like state to a
quark gas-like state in the collision system and indicates that the hadronic
interactions play an important role in this period. At the RHIC and LHC, all
types of chemical potentials become small and tend to zero at very high energy,
which confirms that the collision system possibly changes completely from the
hadron-dominant liquid-like state to the quark-dominant gas-like state and the
partonic interactions possibly play a dominant role at the LHC.
