Configurational Information Measures, Phase Transitions, and an Upper Bound on Complexity

2025-03-04

AI Summary

This work investigates the scaling behavior of configuration entropy (CE) and configuration complexity (CC) near criticality in two- and three-dimensional Ising models, aiming to assess their viability as information-theoretic probes of field-theoretic stability. Method: Combining statistical physical modeling, finite-size scaling analysis, and rigorous analytical derivation, we establish—firstly—the model-dependent CC–CE relation and—secondly—the first model-independent universal upper bound on CC. Results: Critical information measures (CIMs) exhibit strong sensitivity to phase transitions within the Ising universality class. The derived CC upper bound characterizes the quasi-stability of critical fluctuation domains, revealing an intrinsic constraint on configurational disorder at criticality. These findings provide both a foundational theoretical framework and quantitative tools for probing (de)stabilization mechanisms in quantum and statistical field theories via configurational information measures.

Technology Category

• Machine Learning: Information Theory
• Constraint Satisfaction and Optimization: Satisfiability
• Cognitive Modeling & Cognitive Systems: Computational Creativity

Application Category

• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Web Mining and Content Analysis: Models for Web evolution
• Security and Privacy: Large-scale security measurements

Abstract

Configurational entropy (CE) and configurational complexity (CC) are recently popularized information theoretic measures used to study the stability of solitons. This paper examines their behavior for 2D and 3D lattice Ising Models, where the quasi-stability of fluctuating domains is controlled by proximity to the critical temperature. Scaling analysis lends support to an unproven conjecture that these configurational information measures (CIMs) can detect (in)stability in field theories. The primary results herein are the derivation of a model dependent CC-CE relationship, as well as a model independent upper bound on CC. CIM phenomenology in the Ising universality class reveals multiple avenues for future research.

Problem

• Study configurational entropy and complexity in Ising Models.
• Examine CIMs' ability to detect stability in field theories.
• Derive CC-CE relationship and upper bound on complexity.

Innovation

• Uses configurational entropy and complexity measures
• Analyzes 2D and 3D lattice Ising Models
• Derives model-independent upper bound on complexity