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The time evolution of the expanding Colorless Partonic Matter, created inUltra-Relativistic Heavy Ion Collisions and undergoing the confining phasetransition towards a Hadronic Gas, is discussed in the context of a unifiedmodel combining our Colorless QCD-MIT Bag Model with the boost invariantBjorken expansion. The Bjorken Equation in the case of a longitudinal expansionscenario of a non-ideal relativistic medium in finite volume is solved usingcertain initial conditions $(\tau_i,T(\tau_i))$ and their effect is studied indetail. The evolution of the temperature as a function of the proper time$T(\tau,V)$ is then obtained at different volumes. Different timescharacterising different scales of the whole time evolution, like the time ofthe finite volume transition point $\tau_0(V)$, the hadronic time $\tau_H(V)$at which the hadronization is completed, the lifetime of the Colorless PartonicPlasma $\Delta \tau_{CPP}(V)$ and the lifetime of the confining phasetransition $\Delta \tau_{PT}(V)$ are calculated and their finite size scalingproperties are studied in detail. New finite size scaling laws are derived.Also, the time evolution of some Thermal Response Functions as the orderparameter $\mathcal{H}(\tau,V)$, energy density $\epsilon(\tau,V)$, pressure$\mathscr{P}(\tau,V)$ and the sound velocity $\mathscr{C}_{s}(\tau,V)$ areinvestigated and studied in detail. We find that the time evolution of oursystem is really affected by the colorlessness requirement and the initialconditions of the partonic matter: the closer the volume is to thethermodynamic limit, the longer are the times and the lifetimes of the system.A detailed analysis of the temporal decreasing, in negative power, of theenergy density $\epsilon(\tau,V) \propto \tau^{-\theta}$ in each of the threestages of the Bjorken expansion is carried out.

Finite Size Scaling in Time Evolution During the Colorless-QCD Confining Phase Transition