  In the context of closed quantum systems, when a system prepared in its
ground state undergoes a sudden quench, the resulting Loschmidt echo can
exhibit zeros, resembling the Fisher zeros in the theory of classical
equilibrium phase transitions. These zeros lead to nonanalytical behavior of
the corresponding rate function, which is referred to as \textit{dynamical
quantum phase transitions} (DQPTs). In this work, we investigate DQPTs in the
context of open quantum systems that are coupled to both Markovian and
non-Markovian dephasing baths via a conserved quantity. The general framework
is corroborated by studying the non-equilibrium dynamics of a transverse-field
Ising ring. We show the robustness of DQPT signatures under the action of both
engineered dephasing baths, independently on how strongly they couple to the
quantum system. Our theory provides insight on the effect of non-Markovian
environments on DQPTs.
