  In general, classical fully-connected systems are known to undergo violent
relaxation. This phenomenon refers to the relaxation of observables to
stationary, non-thermal, values on a finite timescale, despite their long-time
dynamics being dominated by mean-field effects in the thermodynamic limit.
Here, we analyze the ``quantum" violent relaxation by studying the dynamics of
generic many-body systems with two-body, all-to-all, interactions in the
thermodynamic limit. We show that, in order for violent relaxation to occur
very specific conditions on the spectrum of the mean-field effective
Hamiltonian have to be met. These conditions are hardly met and ``quantum"
violent relaxation is observed rarely with respect to its classical
counterpart. Our predictions are validated by the study of a spin model which,
depending on the value of the coupling, shows a transition between
violent-relaxation and a generic prethermal phase. We also analyze a spin
version of the quantum Hamiltonian-Mean-Field model, which is shown not to
exhibit violent-relaxation. Finally, we discuss how the violent-relaxation
picture emerges back in the classical limit. Our results demonstrate how, even
in the mean-field regime, quantum effects have a rather dramatic impact on the
dynamics, paving the way to a better understanding of light-matter coupled
systems.
