Unveiling the Link between Complexity and Symmetry: Statistical Asymmetry

TL;DR

This paper proposes that statistical asymmetry, or symmetry breaking, can serve as a unifying principle to quantify and understand the concept of complexity across various fields, providing a general methodology and explicit formulas.

Contribution

It introduces a unified framework based on statistical asymmetry to characterize complexity, bridging different existing measures with explicit expressions.

Findings

Statistical asymmetry effectively captures different complexity measures.

A general methodology for quantifying complexity via symmetry breaking is outlined.

Explicit formulas are provided for key cases of complexity measurement.

Abstract

The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed measurements. While each might be appropriated to the problems it addresses, the lack of an underlying fundamental principle prevents the development of a unified theory. Here it is shown that the statistics of the amount of symmetry broken by systems can be used as such unifying principle. A general methodology is outlined and explicit expressions are given for cases in which it can capture the behavior of the two main groups of complexities currently in use. The presented results demonstrate that statistical asymmetry is an appropriate foundation for characterizing the general concept of complexity.