Power Laws Associated with Self-Organized Criticality: A Comparison of Empirical Data with Model Predictions

TL;DR

This study compares empirical data from various fields with self-organized criticality models, finding that most phenomena analyzed are consistent with SOC predictions, though some discrepancies exist due to methodological limitations.

Contribution

It provides a comprehensive comparison of empirical size distributions with SOC model predictions across multiple disciplines, highlighting where models align or diverge.

Findings

80% of analyzed phenomena are consistent with SOC predictions

Solar flares, earthquakes, and forest fires match theoretical power law slopes

Some phenomena show inconclusive results due to data and methodological issues

Abstract

We investigate the relevance of {\sl self-organized criticality (SOC)} models in previously published empirical datasets, which includes statistical observations in astrophysics, geophysics, biophysics, sociophysics, and informatics. We study 25 interdisciplinary phenomena with five different event detection and power law fitting methods. The total number of analyzed size distributions amounts to 64 cases, of which 80\% are found to be nearly consistent ($\alpha_s=1.99\pm0.30$) with the SOC model predictions. The fractal-diffusive SOC model predicts power law slopes of $\alpha_F=(9/5)=1.80$ for the flux $F$, $\alpha_E=(5/3)\sim1.67$ for the fluence or energy $E$, and $\alpha_T=2.00$ for the avalanche duration $T$. We find that the phenomena of solar flares, earthquakes, and forest fires are consistent with the theoretical predictions, while the size distributions of other phenomena are not conclusive due to neglected background treatment, inadequacy of power law fitting range, small-number statistics, and finite-system size effects.