Dynamically Multivalued Self-Organisation and Probabilistic Structure Formation Processes

The unreduced, universally nonperturbative analysis of arbitrary many-body interaction process reveals the irreducible, purely dynamic source of randomness. It leads to the universal definition of real system complexity, where the internally chaotic self-organisation emerges as a characteristic case of complex interaction dynamics. One obtains the causally complete description of the world structure emergence, from elementary particles to consciousness, including practically important and fundamentally substantiated propositions for self-formation research and applications. Introduction Any structure formation process originates in the underlying interactions. A generic interaction is described mathematically by a nonintegrable dynamic equation, which constitutes the unreduced formulation of the many-body problem. Not only it cannot be solved within the conventional theory framework, but the latter does not provide, in general, any sound ideas about the true meaning of “nonintegrability”. Various approximations, always reduced to a version of perturbation theory, are then used to transform the problem into an integrable model of the real system that does possess a closed, or “exact”, solution, but lacks some essential properties of structure formation, among which the autonomous system creativity, i.e. explicit structure emergence without its artificial insertion in another form, is of particular interest for understanding of self-formation processes, ubiquitous in living nature and now also intensively studied in artificially designed, often small-scale systems. In this report we describe a recently elaborated, universally applicable method of solution of the unreduced many-body problem and show that the obtained nonperturbative, truly general problem solution possesses the quality of autonomous creativity, inevitably absent in the conventional, reduced models and perturbative solutions. This essential quality of real structure formation emerges together with the universally valid concept of dynamic complexity and chaoticity based on the key property of dynamic multivaluedness and entanglement of the unreduced problem solution missing in its reduced models (including the conventional versions of “complexity”, “chaoticity”, and “self-organisation”) [1-5]. We then describe the main properties of the unreduced dynamic complexity and the ensuing applications to various natural and artificial structure formation processes. Unreduced Analysis of Arbitrary Many-Body Interaction Problem We start with the most general formulation of a problem of interaction within a many-component system [2], in the form of existence equation that generalises various particular equations: ( ) ( ) ( ) ( ) Q E Q q q V q h N