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Entropy

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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...

Entropy

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Related Experiment Video

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Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

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Which Similarity-Sensitive Entropy (Sentropy)?

Phuc Nguyen¹, Josiah Couch¹, Rahul Bansal¹

¹Department of Pathology, Beth Israel Deaconess Medical Center, Boston, MA 02215.

|November 26, 2025

Summary

This summary is machine-generated.

This study compares two entropy measures, Leinster-Cobbold-Reeve (LCR) and Vendi Score (VS), finding they capture different information. LCR is generally favored for similarity-based entropy calculations, while VS has specific applications.

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Area of Science:

Information Theory
Data Science
Machine Learning

Background:

Traditional entropy measures quantify information based on element frequencies.
Leinster, Cobbold, and Reeve (LCR) introduced similarity-sensitive entropy (S-entropy) to capture richer information.
The Vendi Score (VS) emerged as an alternative, prompting a comparison with LCR.

Purpose of the Study:

To compare the Leinster-Cobbold-Reeve (LCR) method and the Vendi Score (VS) for quantifying system entropy.
To determine the practical implications and optimal use cases for LCR and VS.
To analyze the conceptual, analytical, and experimental differences between LCR and VS.

Main Methods:

Conceptual, analytical, and experimental comparisons using 53 machine-learning datasets.
Investigation of the dependence of LCR and VS on similarity scaling and the introduction of "half distance".
Mathematical proof of VS as an upper bound for LCR under specific conditions.

Main Results:

LCR and VS values can differ significantly and capture complementary information.
Both measures are sensitive to similarity scaling, parameterized by "half distance".
VS is proven to be an upper bound for LCR for several Rényi-Hill order parameters.

Conclusions:

VS is preferable for specific interpretations (ur-elements, quantum-like systems).
LCR is generally favored for capturing similarity-encoded information in entropy calculations.
LCR and VS can be complementary at certain "half distances".