  The impact of non-equilibrium effects on the dynamics of heavy-ion collisions
is investigated by comparing a non-equilibrium transport approach, the
Parton-Hadron-String-Dynamics (PHSD), to a 2D+1 viscous hydrodynamical model,
which is based on the assumption of local equilibrium and conservation laws.
Starting the hydrodynamical model from the same non-equilibrium initial
condition as in the PHSD, using an equivalent lQCD Equation-of-State (EoS), the
same transport coefficients, i.e. shear viscosity $\eta$ and the bulk viscosity
$\zeta$ in the hydrodynamical model, we compare the time evolution of the
system in terms of energy density, Fourier transformed energy density, spatial
and momentum eccentricities and ellipticity in order to quantify the traces of
non-equilibrium phenomena. In addition, we also investigate the role of initial
pre-equilibrium flow on the hydrodynamical evolution and demonstrate its
importance for final state observables. We find that due to non-equilibrium
effects, the event-by-event transport calculations show large fluctuations in
the collective properties, while ensemble averaged observables are close to the
hydrodynamical results.
