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 to describe the dissipative dynamics in the presence of phase coexistence. Metastability in Markovian open quantum systems turns out to be a nontrivial problem due to the separation of timescales in the dissipative dynamics. Typically, the Lindblad equation is able to describe the short-time dynamics during which the system relaxes to a metastable state, while it fails to describe the long-time ergodic dynamics that drives relaxation to the true equilibrium state. We show how to describe the full dynamics in terms of an effective Lindblad equation valid in both regimes. 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.