  Here we provide a theoretical framework to analyze discrete time-crystalline
phases (DTC) in open quantum many-body systems. As a particular realization, we
choose a quantum many-body system that exhibits cascaded prethermalization .
The analysis uses a fluctuation-regulated quantum master equation. The master
equation captures the dissipative effects of the drive and dipolar coupling on
the dynamics regularized by the thermal fluctuations. We find that the
dissipators from the drive and the dipolar interactions lend stability to the
dynamics and are directly responsible for the robustness. Specifically, we find
that longer fluctuation correlation time enhances the stability of DTC. Our
results are in good agreement with the experiments. Finally, we show and
quantify how the DTC performance degrades with temperature.
