Speeding up Pontus-Mpemba effects via dynamical phase transitions

We demonstrate that open quantum systems exhibiting dynamical phase transitions (DPTs) allow for efficient protocols implementing the Pontus-Mpemba effect. The relaxation speed-up toward a predesignated target state is tied to the existence of a long metastable time window preceding the DPT and can be exploited in applications to systematically optimize quantum protocols. As paradigmatic example for the connection between DPTs and quantum Mpemba effects, we study one-dimensional (1D) interacting lattice fermions corresponding to a dissipative variant of the Gross-Neveu (GN) model.