Exponentially slow mixing and hitting times of rare events for a reaction–diffusion model

. We consider the superposition of symmetric simple exclusion dynamics speeded-up in time, with spin-flip dynamics in a one-dimensional interval with periodic boundary conditions. We show that the mixing time has an exponential lower bound in the system size if the potential of the hydrodynamic equation has two or more local minima. We also apply our estimates to show that the normalized hitting times of rare events converge to a mean one exponential random variable if the potential has a unique minimum. deviation the quasi-potential and solutions to the