Macrodynamic Cooperative Complexity of Information Dynamics

Abstract

The introduced concept and measure of macrocomplexity (MC) arise in an irreversible macrodynamic cooperative process and determine the process components ability to assemble into an integrated system. MC serves as a common indicator of the origin of the cooperative complexity measured by the specific entropy speed per assembled volume, rather than the entropy, as it has been accepted before. The MC cooperative mechanism is studied using the variation principle (VP) of information macrodynamics (IMD), applied to a complex system with the macrolevel dynamics and random microlevel stochastics and different forms of physical and virtual transitions of information. This principle describes a transition from a local unstable process movement to a local stable process — the former is associated with the current influx of information that precedes cooperation, and the latter is continued after the cooperation with incoming information and its accumulation. This transition enables the production of the cooperative phenomena and, in particular, the contributions from different superimposing processes, which are measured by the MC. MC, arising as an indicator of these phenomena at the unification (or decomposition) of the system processes, is defined by the invariant information measure, allowing for both analytical formulation and computer evaluation. An optimal multi-dimensional consolidation process, satisfying the VP, forms the information hierarchical network (IN) consisting of the model eigenvalues sequential cooperation in triples. The MC of such an optimal cooperative triplet structure is measured by the IN triplet code (as an algorithm of the minimal program, which evaluates the IN hierarchical structure by the triplet information contributions in bits of information). The distributed IN allows for the automatic arrangement and measurement of the MC-local complexities in a multi-dimensional cooperative process, taking into account the MC time-space locations and mutual dependencies, and providing the MC hierarchical invariant information measure by quantity and quality in the triplet code. The MC is connected to Kolmogorov (K) complexity, which measures a deterministic order over a stochastic disorder by a minimal program. The MC specific consists of providing a computable complexity measure of a cooperative dynamic irreversible process, as an opposite to the K incomputability.