Equilibrium perturbations for stochastic interacting systems

We consider the equilibrium perturbations for two stochastic systems: d-dimensional generalized exclusion process and one-dimensional chain of anharmonic oscillators. add a perturbation order N−α to profile speed up by N1+κ parameters 0<κ≤α. Under some additional constraints on κ α, we show perturbed quantities evolve according Burgers equation in process, decoupled equations chain, both smooth regime.