Towards a common thread in Complexity: an accuracy-based approach

TL;DR

This paper introduces an accuracy-based approach to understanding complexity in systems, showing that matrix element fluctuations can be modeled by a unified mathematical framework with a single parameter, revealing universal classes.

Contribution

It proposes a novel accuracy-based method to characterize system complexity and universality classes through a unified diffusion model of matrix elements.

Findings

Diffusion of matrix elements can be described by a single-parameter mathematical formulation.

System information influences the model through one key parameter.

Physical properties can be classified into infinite universality classes based on this framework.

Abstract

The complexity of a system, in general, makes it difficult to determine some or almost all matrix elements of its operators. The lack of accuracy acts as a source of randomness for the matrix elements which are also subjected to an external potential due to existing system conditions. The fluctuation of accuracy due to varying system-conditions leads to a diffusion of the matrix elements. We show that, for the single well potentials, the diffusion can be described by a common mathematical formulation where system information enters through a single parameter. This further leads to a characterization of physical properties by an infinite range of single parametric universality classes.