  We examine how the presence of an excited state quantum phase transition
manifests in the dynamics of a many-body system subject to a sudden quench.
Focusing on the Lipkin-Meshkov-Glick model initialized in the ground state of
the ferromagnetic phase, we demonstrate that the work probability distribution
displays non-Gaussian behavior for quenches in the vicinity of the excited
state critical point. Furthermore, we show that the entropy of the diagonal
ensemble is highly susceptible to critical regions, making it a robust and
practical indicator of the associated spectral characteristics. We assess the
role that symmetry breaking has on the ensuing dynamics, highlighting that its
effect is only present for quenches beyond the critical point. Finally, we show
that similar features persist when the system is initialized in an excited
state and briefly explore the behavior for initial states in the paramagnetic
phase.
