  Imposing an equilibrium between the thermal pressure of deconfined quarks and
gluons and the dynamical compression pressure exercised by in-flowing nuclear
matter, we study the initial thermal conditions reached in a quark-gluon plasma
fireball formed in a relativistic heavy ion collision. We show that entropy is
produced primarily in the pre-equilibrium stage of the reaction. We test our
approach, comparing our results with the S-W/Pb collision results at 200 GeV A
and find a surprising degree of agreement assuming about 50% stopping. We apply
our method to a determination of the conditions in collisions of Au-Au at 11
GeV A and Pb-Pb at 157 GeV A, assuming full stopping of momentum, energy and
baryon number. Our detailed results directly determine the spectral shape and
abundance of (strange) hadrons and electromagnetic probes (photons, dileptons)
produced in the collision, and we explore specific experimental consequences.
