Long range correlations and the onset of chemical instabilities

Recent analyses of fluctuations in non-equilibrium systems by Prigogine, Malek-Mansour and Nicolis have indicated the existence of a minimal coherence length beyond which fluctuations can amplify and induce instabilities at a macroscopic scale. Conversely, this observation suggests the emergence of long range spatial correlations in systems undergoing non-equilibrium unstable transitions. In the present paper, this problem is analyzed for reaction-diffusion systems and illustrated on a specific model. The existence of diverging form factors and of long range correlations is established. The connection between the multi-variate master equation and the local equation developed recently by Prigogine, Malek-Mansour and Nicolis is discussed.