  By applying the closed-time-path Green function formalism to the chiral
dynamical model based on an effective Lagrangian of chiral quarks with the
nonlinear-realized meson fields as bosonized auxiliary fields, we then arrive
at a chiral thermodynamic model for the meson fields with finite temperature.
Particular attention is paid to the spontaneous chiral symmetry breaking and
restoration from the dynamically generated effective composite Higgs potential
of meson fields at finite temperature. It is shown that the minimal condition
of the effective composite Higgs potential of meson fields leads to the
thermodynamic gap equation at finite temperature, which enables us to
investigate the critical behavior of the effective chiral thermodynamical model
and to explore the QCD phase transition. After fixing the free parameters in
the effective chiral Lagrangian at low energies with zero temperature, we
determine the critical temperature of the chiral symmetry restoration and
present a consistent prediction for the thermodynamical behavior of several
physically interesting quantities, which include the vacuum expectation value
$v_o(T)$, quark condensate $<\bar{q}q>(T)$, pion decay constant $f_\pi(T)$ and
pion meson mass $m_{\pi}(T)$. In particular, it is also shown that the
thermodynamic scaling behavior of these quantities becomes the same near the
critical point of phase transition.
