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We investigate the dissipative dynamics yielded by the Lindblad equationwithin the coexistence region around a first order phase transition. Inparticular, we consider an exactly-solvable fullyconnected quantum Ising modelwith n-spin exchange (n > 2) - the prototype of quantum first order phasetransitions - and several variants of the Lindblad equations. We show thatphysically sound results, including exotic non-equilibrium phenomena like theMpemba effect, can be obtained only when the Lindblad equation involves jumpoperators defined for each of the coexisting phases, whether stable ormetastable.

Lindblad dissipative dynamics in presence of phase coexistence