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Entropy Treatment of Evolution Algebras
Farrukh Mukhamedov1, Izzat Qaralleh2
1Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al Ain P.O. Box 15551, United Arab Emirates.
Entropy (Basel, Switzerland)
|May 28, 2022
Summary
This study introduces entropy for Markov evolution algebras to analyze S-evolution algebra isomorphism. Relative entropy further aids in understanding the structural relationships within these algebraic systems.
Area of Science:
- Algebraic structures
- Mathematical analysis
Background:
- Evolution algebras are algebraic structures with applications in various fields.
- Understanding the isomorphism of these algebras is crucial for classification and application.
- Markov evolution algebras represent a specific class with unique properties.
Purpose of the Study:
- To introduce and utilize the concept of entropy for Markov evolution algebras.
- To investigate the isomorphism of S-evolution algebras using entropy measures.
- To explore the application of relative entropy in studying S-evolution algebra isomorphism.
Main Methods:
- Definition of a family of Markov evolution algebras via Hadamard product of structural matrices.
- Application of entropy of Markov evolution algebras to study isomorphism.
- Utilizing the concept of relative entropy for isomorphism analysis.
Main Results:
- A novel method for treating the isomorphism of S-evolution algebras is presented.
- The entropy of Markov evolution algebras is shown to be a tool for isomorphism study.
- Relative entropy provides an additional perspective on the isomorphism of S-evolution algebras.
Conclusions:
- Entropy measures offer a powerful framework for analyzing the isomorphism of S-evolution algebras.
- The Hadamard product construction yields a relevant family of Markov evolution algebras.
- This work contributes to the structural understanding of S-evolution algebras.
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