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Diversity as an entropic measure derived from entropiclike functionals.
Eugenio E Vogel1,2, Constantino Tsallis3,4,5, Gonzalo Saravia6
1Universidad de La Frontera, Departamento de Ciencias Físicas, Temuco, Chile.
Physical Review. E
|May 16, 2026
Summary
We introduce diversity, an entropy-related function, derived from Shannon entropy. This new measure shows sharper responses at critical points in both equilibrium and non-equilibrium systems.
Area of Science:
- Information Theory
- Statistical Mechanics
- Complex Systems Analysis
Background:
- Entropy functionals are fundamental in quantifying uncertainty and information.
- Diversity, an entropy-related function, offers a novel perspective on system complexity.
- Understanding system dynamics requires robust analytical tools applicable to both equilibrium and non-equilibrium states.
Purpose of the Study:
- To derive and define a new entropy-related function called diversity.
- To explore the relationship between diversity, Shannon entropy, and Jensen-Shannon divergence.
- To apply diversity and Shannon entropy to analyze equilibrium and non-equilibrium systems.
Main Methods:
- Derivation of diversity using two forms of Shannon entropy.
- Expressing diversity as an exponential of Shannon entropy differences.
- Utilizing Jensen-Shannon divergence as a function dependent on diversity.
- Applying these concepts to the Ising model (equilibrium) and a seismic region in Alaska (non-equilibrium).
Main Results:
- Two distinct derivations of the diversity function are presented.
- The Jensen-Shannon divergence is shown to be dependent solely on diversity.
- Diversity provides sharper responses at critical points in analyzed systems.
- Diversity reveals more detailed texture in the general trends of both equilibrium and non-equilibrium systems.
Conclusions:
- Diversity is a robust entropy-related function with clear mathematical derivations.
- Its application demonstrates superior sensitivity at critical points compared to traditional entropy measures.
- Diversity offers enhanced insights into the dynamics of complex systems, irrespective of their equilibrium state.
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