  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 $N^{-\alpha}$ to the
equilibrium profile and speed up the process by $N^{1+\kappa}$ for parameters
$0<\kappa\le\alpha$. Under some additional constraints on $\kappa$ and
$\alpha$, 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.
