Lindblad dissipative dynamics in the presence of phase coexistence

We investigate the dissipative dynamics yielded by the Lindblad equation within the coexistence region around a first-order phase transition. In particular, we consider an exactly solvable, fully connected quantum Ising model with n-spin exchange (n>2) - the prototype of quantum first-order phase transitions - and several variants of the Lindblad equations. We show that physically sound results, including exotic nonequilibrium phenomena such as the Mpemba effect, can be obtained only when the Lindblad equation involves jump operators defined for each of the coexisting phases, whether stable or metastable.