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A Maximum Entropy Method for the Prediction of Size Distributions
Cornelia Metzig1,2, Caroline Colijn3,4
1Business School, Imperial College London, London SW7 2AZ, UK.
Entropy (Basel, Switzerland)
|December 8, 2020
Summary
We introduce a novel entropy maximization method to determine system size and network degree distributions. This approach accurately predicts power-law exponents and exponential cutoffs, validated by simulations.
Area of Science:
- Statistical Mechanics
- Network Science
- Information Theory
Background:
- Deriving stationary distributions is crucial for understanding complex systems.
- Existing methods often require specific model assumptions.
- Entropy maximization offers a universal framework for distribution analysis.
Purpose of the Study:
- To develop a general method for deriving stationary size and degree distributions.
- To apply Gibbs-Shannon entropy maximization to systems with particle/node and edge turnover.
- To validate the method against established models and simulations.
Main Methods:
- Utilizing Gibbs-Shannon entropy maximization.
- Applying the method to preferential attachment models with exit dynamics.
- Deriving power-law exponents and exponential cutoffs from mean size/degree and turnover rate.
Main Results:
- The entropy maximization method successfully derives stationary size and degree distributions.
- The method accurately predicts power-law exponents and exponential cutoffs.
- Reproduces known distributions like Maxwell-Boltzmann and Barabasi-Albert.
Conclusions:
- Gibbs-Shannon entropy maximization provides a powerful, unified approach for distribution analysis in diverse systems.
- The method offers a principled way to derive key distribution parameters.
- This work bridges statistical mechanics, network science, and information theory.
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