  We investigate propagation of perturbations of equilibrium states for a wide
class of 1D interacting particle systems. The class of systems considered
incorporates zero range, $K$-exclusion, mysanthropic, `bricklayers' models, and
much more. We do not assume attractivity of the interactions. We apply Yau's
relative entropy method rather than coupling arguments.
  The result is \emph{partial extension} of T. Sepp\"al\"ainen's recent paper.
For $0<\beta<1/5$ fixed, we prove that, rescaling microscopic space and time by
$N$, respectively $N^{1+\beta}$, the macroscopic evolution of perturbations of
microscopic order $N^{-\beta}$ of the equilibrium states is governed by
Burgers' equation. The same statement should hold for $0<\beta<1/2$ as in
Sepp\"al\"ainen's cited paper, but our method does not seem to work for
$\beta\ge1/5$.
