  We study the evolution of a small perturbation of the equilibrium of a
totally asymmetric one-dimensional interacting system. The model we take as
example is Hammersley's process as seen from a tagged particle, which can be
viewed as a process of interacting positive-valued stick heights on the sites
of Z. It is known that under Euler scaling (space and time scale n) the
empirical stick profile obeys the Burgers equation. We refine this result in
two ways: If the process starts close enough to equilibrium, then over times
n^\nu for 1\le\nu<3, and up to errors that vanish in hydrodynamic scale, the
dynamics merely translates the initial stick configuration. A time evolution
for the perturbation is visible under a particular family of scalings: over
times n^\nu, 1<\nu<3/2, a perturbation of order n^(1-\nu) from equilibrium
follows the inviscid Burgers equation. The results for the stick model are
derived from asymptotic results for tagged particles in Hammersley's process.
