  We present a study of the spatial correlation functions of a one-dimensional
reaction-diffusion system in both equilibrium and out of equilibrium. For the
numerical simulations we have employed the Gillespie algorithm dividing the
system in cells to treat diffusion as a chemical process between adjacent
cells. We find that the spatial correlations are spatially short ranged in
equilibrium but become long ranged in nonequilibrium. These results are in good
agreement with theoretical predictions from fluctuating hydrodynamics for a
one-dimensional system and periodic boundary conditions.
