  Based on quantum statistical mechanics we show that the $SU(3)$ color singlet
ensemble of a quark-gluon gas exhibits a $Z(3)$ symmetry through the normaized
character in fundamental representation and also becomes equivalent, within a
stationary point approximation, to the ensemble given by Polyakov Loop. Also
Polyakov Loop gauge potential is obtained by considering spatial gluons along
with the invariant Haar measure at each space point. The probability of the
normalized character in $SU(3)$ vis-a-vis Polyakov Loop is found to be maximum
at a particular value exhibiting a strong color correlation. This clearly
indicates a transition from a color correlated to uncorrelated phase or
vise-versa. When quarks are included to the gauge fields, a metastable state
appears in the temperature range $145\le T({\rm{MeV}}) \le 170$ due to the
explicit $Z(3)$ symmetry breaking in the quark-gluon system. Beyond $T\ge 170$
MeV the metastable state disappears and stable domains appear. At low
temperature a dynamical recombination of ionized $Z(3)$ color charges to a
color singlet $Z(3)$ confined phase is evident along with a confining
background that originates due to circulation of two virtual spatial gluons but
with conjugate $Z(3)$ phases in a closed loop. We also discuss other possible
consequences of the center domains in the color deconfined phase at high
temperature.
