Power-law ansatz in complex systems: Excessive loss of information

Area of Science:

• Complex Systems
• Statistical Physics
• Data Analysis

Background:

• Power-law relations are ubiquitous in empirical data, often sought by physicists to reveal underlying simple laws.
• However, many reported power laws lack robust statistical and mechanistic support, with discrepancies often attributed to finite-size effects.
• Existing models struggle to explain the transition between different driving mechanisms observed in complex systems.

Purpose of the Study:

• To propose and validate a rigorous experimental and statistical framework for assessing power-law distributions.
• To investigate the transition from multiple power-law behaviors to a single bona fide power law in a simulated complex system.
• To demonstrate the influence of interactions on macroscopic behavior and the utility of the Akaike information criterion (AIC) in model selection.

Main Methods:

• Simulating a complex system by crumpling two different sheets together, generating "crumple sound" data.
• Analyzing the probability function of crumple sound occurrence rate and pulse intensity.
• Employing the Akaike information criterion (AIC) for rigorous statistical model comparison and information loss assessment.

Main Results:

• The probability function of crumple sound transitions from two distinct power-law terms to a single, genuine power law as compaction increases.
• This transition demonstrates how interactions between driving mechanisms can lead to emergent macroscopic behavior.
• The AIC successfully identified genuine power laws and flagged other established laws (Gutenberg-Richter, scale-free models) as information-lossy.

Conclusions:

• Interactions in complex systems can drive the emergence of a single power law from multiple underlying mechanisms.
• The proposed experimental and statistical approach, centered on AIC, provides a robust method for validating power-law claims.
• AIC serves as a crucial tool for balancing model simplicity and goodness-of-fit, highlighting information loss in potentially oversimplified models.