  We introduce an event-by-event perturbative-QCD + saturation + hydro ("EKRT")
framework for ultrarelativistic heavy-ion collisions, where we compute the
produced fluctuating QCD-matter energy densities from next-to-leading order
perturbative QCD using a saturation conjecture to control soft particle
production, and describe the space-time evolution of the QCD matter with
dissipative fluid dynamics, event by event. We perform a simultaneous
comparison of the centrality dependence of hadronic multiplicities, transverse
momentum spectra, and flow coefficients of the azimuth-angle asymmetries,
against the LHC and RHIC measurements. We compare also the computed
event-by-event probability distributions of relative fluctuations of elliptic
flow, and event-plane angle correlations, with the experimental data from Pb+Pb
collisions at the LHC. We show how such a systematic multi-energy and
multi-observable analysis tests the initial state calculation and the
applicability region of hydrodynamics, and in particular how it constrains the
temperature dependence of the shear viscosity-to-entropy ratio of QCD matter in
its different phases in a remarkably consistent manner.
