Effective kinetic description of event-by-event pre-equilibrium dynamics in high-energy heavy-ion collisions

We develop a macroscopic description of the space-time evolution of the energy-momentum tensor during the pre-equilibrium stage of a high-energy heavy-ion collision. Based on a weak coupling effective kinetic description of the microscopic equilibration process (\`a la ``bottom-up''), we calculate the nonequilibrium evolution of the local background energy-momentum tensor as well as the nonequilibrium linear response to transverse energy and momentum perturbations for realistic boost-invariant initial conditions for heavy-ion collisions. We demonstrate how this framework can be used on an event-by-event basis to propagate the energy-momentum tensor from far-from-equilibrium initial-state models to the time ₇ₘ₃ₑ₎ when the system is well described by relativistic viscous hydrodynamics. The subsequent hydrodynamic evolution becomes essentially independent of the hydrodynamic initialization time ₇ₘ₃ₑ₎ as long as ₇ₘ₃ₑ₎ is chosen in an appropriate range where both kinetic and hydrodynamic descriptions overlap. We find that for s₍₍=2. 760. 16em{0ex}0. 16em{0ex}TeV central Pb-Pb collisions, the typical timescale when viscous hydrodynamics with shear viscosity over entropy ratio /s=0. 16 becomes applicable is ₇ₘ₃ₑ₎10. 16em{0ex}fm/c after the collision.