Laws and events: The dynamical basis of self-organization

Abstract

Traditionally, self-organization has been studied using macroscopic phenomenological descriptions. Recent computer simulations show that "dissipative structures" may be obtained through dynamical programs without any macroscopic assumptions. Self-organization is rooted in dynamics. This leads to the question, "what type of dynamical laws permit self-organization?" The answer refers to unstable dynamical systems, which were widely studied after the pioneering work of Kolmogorov. We concentrate our work on large Poincaré systems with continuous spectrum of the Liouville operator, a generalization of Poincaré's nonintegrable systems. Examples are collisions or quantum jumps. We show that resonances lead to a dynamics of correlations, which can be analyzed using our recent theory of subdynamics. We decompose the dynamical evolution into a set of independent processes. As an example, we study radiation processes as well as the transformation of classical dynamics information into order or disorder processes. We show that in quantum mechanics, our approach leads to a reinterpretation of the collapse of the wave function, owing to the dynamical nature of the system and not to human measurement.