  We study a nonequilibrium mean field Ising model in the low temperature phase
regime, where metastable equilibrium states develop a cuspidal (spinodal)
singularity. We focus on celebrated Glauber dynamics, and design a contact
Hamiltonian flow which captures some of its rough features in this regime. We
prove, however, that there is an inevitable discrepancy between the scaling
laws for the relaxation time in the Glauber and the contact Hamiltonian
dynamical systems.
