Informational and entropic criteria of self-organization

TL;DR

This paper investigates qualitative informational and entropic criteria for self-organization in open systems, defining specific entropy ranges that indicate self-affinity and self-similarity, validated through fractal analysis.

Contribution

It introduces a novel approach using information and entropy values as criteria for self-organization, with specific entropy thresholds identified and validated against fractal structures.

Findings

Self-organization occurs when normalized entropy S is between 0.567 and 0.806.

Defined information and entropy values serve as criteria for self-affinity and self-similarity.

Validated criteria through calculations on hierarchical fractal sets.

Abstract

The work is devoted to study of the following problem: can we use any qualitative criteria for realization of such universal phenomenon as self-organization in open systems? We have defined values of information at fixed points of probability function of density of information and entropy. Physical meaning of these values as criteria of self-affinity and self-similarity in chaotic processes have been explained. We have shown that self-organization occurs if normalized information entropy S belongs to the range 0.567<S<0.806. The validity of these findings is confirmed by calculation of value of S for hierarchical sets of well-known fractals.