Equilibrium perturbations for stochastic interacting systems

We consider the equilibrium perturbations for two stochastic systems: the d-dimensional generalized exclusion process and the one-dimensional chain of anharmonic oscillators. We add a perturbation of order $N^{-α}$ to the equilibrium profile and speed up the process by $N^{1+κ}$ for parameters 0 < κ ≤ α. Under some additional constraints on κ and α, we show the perturbed quantities evolve according to the Burgers equation in the exclusion process, and to two decoupled Burgers equations in the anharmonic chain, both in the smooth regime.