  The phase transition for a finite volume system that incorporates the
Polyakov loops and maintains the colorless state is explored using the
Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model. The order parameter for
Polyakov loops is demonstrated to signal the appearance of a transition for
$SU(3)_{c}$ analogous to Gross-Witten (GW-) phase transition instead of the
deconfinement phase transition to quark-gluon plasma. The asymptotic
restoration of Polyakov loops is conjectured to be a threshold production for
meta-stable Hagedorn (or semi-QGP) states and this does not imply a direct
deconfinement phase transition. In this context, the GW-like point is the point
where the colorless states switches from the low-lying hadronic states to the
meta-stable high-lying Hagedorn states. The chiral phase transition takes place
within an extended GW-like point depending on the fireball's size. The
deconfinement phase transition is determined by Hagedorn's temperature above
GW-like temperature.
