  The dynamics of relative entropy and $l_{1}$-norm of coherence, as well as,
the Wigner-Yanase-skew and quantum Fisher information are studied for a
time-dependent coupled XY spin chain in presence of a time-dependent transverse
magnetic field. Independent of the initial state of the system and while the
relative entropy of coherence, $l_{1}$-norm of coherence, and quantum Fisher
information are incapable, surprisingly, the dynamic Wigner-Yanase-skew
information can truly spotlight the equilibrium critical point. We also observe
that when the system is quenched to the critical point, these quantities show
suppressions and revivals. Moreover, the first suppression (revival) time
scales linearly with the system size and its scaling ratio is unique for all
quenches independent to the initial phase. This is the promised universality of
the first suppression (revival) time.
