  We study the evolution in equilibrium of the fluctuations for the conserved
quantities of a chain of anharmonic oscillators in the hyperbolic space-time
scaling. Boundary conditions are determined by applying a constant tension at
one side, while the position of the other side is kept fixed. The Hamiltonian
dynamics is perturbed by random terms conservative of such quantities. We prove
that these fluctuations evolve macroscopically following the linearized Euler
equations with the corresponding boundary conditions, even in some time scales
larger than the hyperbolic one.
