Spatial correlations in nonequilibrium reaction-diffusion problems by the Gillespie algorithm.

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 into 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.