Some Historical Remarks and Outlook

Abstract

The reader who has followed us through our book has been most probably amazed by the profound analogies between completely different systems when they pass through an instability. This instability is caused by a change of external parameters and leads eventually to a new macroscopic spatio-temporal pattern of the system. In many cases the detailed mechanism can be described as follows: close to the instability point we may distinguish between stable and unstable collective motions (modes). The stable modes are slaved by the unstable modes and can be eliminated. In general, this leads to an enormous reduction of the degrees of freedom. The remaining unstable modes serve as order parameters determining the macroscopic behavior of the system. The resulting equations for the order parameters can be grouped into a few universality classes which describe the dynamics of the order parameters. Some of these equations are strongly reminiscent of those governing first and second order phase transitions of physical systems in thermal equilibrium. However, new kinds of classes also occur, for instance describing pulsations or oscillations. The interplay between stochastic and deterministic “forces” (“chance and necessity”) drives the systems from their old states into new configurations and determines which new configuration is realized.KeywordsOrder Phase TransitionUnstable ModeExternal ParameterUniversality ClassStable ModeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.