Contact geometric approach to Glauber dynamics near cusp and its limitation

We study nonequilibrium thermodynamic systems in the low temperature phase regime, where metastable equilibrium states develop cuspidal (spinodal) singularity. We focus on the 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.Comment: 15 pages, 2 figure