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Extreme Synergy in the Random-Energy Model.
Vudtiwat Ngampruetikorn1,2, David J Schwab2
1School of Physics, <a href="https://ror.org/0384j8v12">University of Sydney</a>, Sydney, NSW 2006, Australia.
Physical Review Letters
|January 3, 2025
Summary
The random-energy model (REM) demonstrates extreme synergy, enabling a novel secure secret-sharing scheme. This statistical physics model offers optimal information encoding and connects physics to computation.
Area of Science:
- Statistical Physics
- Information Theory
- Computational Science
Background:
- The random-energy model (REM) is a solvable spin-glass model with broad applications.
- Previous applications span protein folding, combinatorial optimization, and many-body localization.
- A novel connection between REM and secret sharing is explored.
Purpose of the Study:
- To derive an analytic expression for mutual information between REM subsystems.
- To formulate a secret-sharing scheme based on REM correlations.
- To determine conditions for secure secret sharing within the REM framework.
Main Methods:
- Derivation of analytic expression for mutual information.
- Formulation of a secret-sharing scheme using REM.
- Analysis of temperature and secret length parameters for security.
- Investigation of a special point for optimal information encoding.
Main Results:
- REM correlations exhibit extreme synergy, analogous to secure secret sharing.
- Specific temperature and secret length ranges for REM security were identified.
- A physically optimal information encoding point in the REM phase diagram was found.
- Thermodynamic limit results align qualitatively with finite system simulations.
Conclusions:
- The REM provides a framework for secure secret sharing with optimal encoding properties.
- Synergistic correlations in many-body systems can be characterized using this new language.
- Information theory serves as a unifying concept linking statistical physics and computation.
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