Scaling theory for nonequilibrium systems

We develop a general scaling theory of one-dimensional systems withN components having applications to disorder-order-transitions or order-order transitions of non-equilibrium systems, such as lasers, hydrodynamical systems and non-equilibrium chemical reactions. We include both cases of soft and hard modes. Since fluctuations play a decisive role at the transition point, we take fully account of them. We start from general equations of motion which contain nonlinear forces (or rates), diffusion terms and fluctuating forces. These equations depend on external parameters. When linearized around their steady state solutions, the equations allow for stable, marginal or unstable solutions. The solutions near critical points are represented as superpositions of marginal solutions, whose amplitudes are determined by comparing the coefficients of the scaling parameter up to third order. The scaling of the fluctuating forces and, in the case of chemical reactions, their correlation functions are derived in detail.