The Approach to Equilibrium: Scaling, Universality and the Renormalisation Group

Abstract

Evidence is accumulating that the long-time behaviour of certain non-equilibrium systems shows scaling behaviour. This assertion is demonstrated in the cases of spinodal decomposition, block copolymer phase separation, crystal growth, and a particular diffusion process which can occur in porous media. These, and hopefully other non-equilibrium problems may be studied by computationally efficient numerical methods, which are based not upon discretising partial differential equations, but upon a coarse-grained description of the dynamics. In the case of non-linear diffusion in a porous medium, it is shown that the renormalisation group can be used to study the long-time behaviour, and to calculate perturbatively the exponents characterising the anomalous diffusion.