Thermalization in ultrarelativistic nuclear collisions. II. Entropy production and energy densities at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider

The dynamics of partons in ultrarelativistic ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$+${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$ collisions in the future collider experiments at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider during the first 3 fm/c is simulated in full six-dimensional phase space within a parton cascade model to compute the entropy production and the space-time-dependent energy densities, temperatures, etc., in the central collision region. The partons' evolution from preequilibrium towards the formation of a thermalized quark-gluon plasma is investigated and compared to the Bjorken scenario. Moreover, an equation of state is extracted together with initial conditions for the further hydrodynamical space-time evolution of the matter. For central ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$+${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$ collisions with $\sqrt{s}=200-6300A$ GeV the predictions for the energy densities and associated temperatures at $t=3\mathrm{}$ fm/c after the first instant of the collisions are $\varepsilon =15-31\mathrm{}$ GeV/${\mathrm{fm}}^3$ and $T=297-343\mathrm{}$ MeV, respectively. The multiplicity of final pions from the plasma is estimated from the amount of entropy produced, yielding a huge $\frac{d{N}^{\left(\pi \right)}}{\mathrm{dy}\simeq 1900-3400}$.