  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 fullyconnected 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 non-equilibrium phenomena like 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.
