  We investigate the quench dynamics of an open quantum system involving a
quantum phase transition. In the isolated case, the quench dynamics involving
the phase transition exhibits a number of scaling relations with the quench
rate as predicted by the celebrated Kibble-Zurek mechanism. In contact with an
environment however, these scaling laws breakdown and one may observe an
anti-Kibble-Zurek behavior: slower ramps lead to less adiabatic dynamics,
increasing thus non-adiabatic effects with the quench time. In contrast to
previous works, we show here that such anti-Kibble-Zurek scaling can acquire a
universal form in the sense that it is determined by the equilibrium critical
exponents of the phase transition, provided the excited states of the system
exhibit singular behavior, as observed in fully-connected models. This
demonstrates novel universal scaling laws granted by a system-environment
interaction in a critical system. We illustrate these findings in two
fully-connected models, namely, the quantum Rabi and the Lipkin-Meshkov-Glick
models. In addition, we discuss the impact of non-linear ramps and finite-size
systems.
