Multiscale Structure of More-than-Binary Variables

TL;DR

This paper refines an information-theoretic formalism to analyze complex multi-component systems, introducing the concept of ancilla components to better understand non-binary relationships and system structure.

Contribution

It introduces the concept of ancilla components to enhance the analysis of multiscale structures in systems, addressing limitations of pairwise decomposition.

Findings

Ancilla components help reveal subtle system structures.

The scheme clarifies the role of non-binary relationships.

Comparison with recent proposals highlights advantages.

Abstract

In earlier work, my colleagues and I developed a formalism for using information theory to understand scales of organization and structure in multi-component systems. One prominent theme of that work was that the structure of a system cannot always be decomposed into pairwise relationships. In this brief communication, I refine that formalism to address recent examples which bring out that theme in a novel and subtle way. After summarizing key points of earlier papers, I introduce the crucial new concept of an ancilla component, and I apply this refinement of our formalism to illustrative examples. The goals of this brief communication are, first, to show how a simple scheme for constructing ancillae can be useful in bringing out subtleties of structure, and second, to compare this scheme with another recent proposal in the same genre.