# Time-dependent Ginzburg-Landau theory of nonequilibrium relaxation

## Abstract

The system is considered which is brought into a state far from thermal equilibrium by a sudden change of independent variables. Its approach towards the equilibrium state is studied introducing nonequilibrium relaxation functions. Near the equilibrium state the lowest-order relaxation functions reduce to the time-dependent pair correlation functions. The relaxation process is especially interesting near a first-order phase transition, where metastable states can occur. Characterization of these states in terms of the nonequilibrium relaxation functions is discussed, and a "constructive" definition of the metastable states in terms of a "flatness" property of the relaxation curve is proposed. In order to give explicit results, the time-dependent Ginzburg-Landau theory is treated in detail, and exact solutions for the relaxation functions are given. If an equilibrium state is described by a real-valued order parameter, the inverse lifetime of a metastable state is determined from the imaginary part of its order parameter. Transition from the "metastable" to the stable state is characterized by fluctuations which increase with time for wave vectors up to some critical value, and later decrease again because of the nonlinearity of the Ginzburg-Landau equations. The validity of these results is discussed with respect to systems with long-range interactions, and also a few remarks are given concerning systems with short-range interactions and the nucleation picture. © 1973 The American Physical Society.