Appearance of correlations and symmetry breaking in non-equilibrium reaction-diffusion systems

Abstract

Using the reaction-diffusion master equation of chemical kinetics, the authors study fluctuations and correlation functions around non-equilibrium steady states. They demonstrate that the underlying Lagrangian description in the Poisson representation possesses in the equilibrium limit an exact symmetry which ensures that statistical mechanics is recovered and that the intrinsically non-equilibrium long-range correlations in these systems vanish. An explicit form for the two-time single-particle correlation function, including both the long-range and short-range contributions, is constructed using mean-field arguments.