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The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
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Group Structure as a Foundation for Entropies.

Henrik Jeldtoft Jensen1,2, Piergiulio Tempesta3,4

  • 1Centre for Complexity Science and Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK.

Entropy (Basel, Switzerland)
|March 28, 2024
PubMed
Summary
This summary is machine-generated.

This study reviews entropy as a functional on probability spaces. It shows how handling non-interacting systems and extensivity enables a systematic classification of entropy

Keywords:
composabilityentropyextensivitygroup theoryinformation theorypower laws

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Area of Science:

  • Thermodynamics
  • Information Theory
  • Mathematical Physics

Background:

  • Entropy has diverse definitions across fields like thermodynamics and data analysis.
  • The proliferation of entropy measures complicates understanding their relative importance and applications.
  • A unified framework is needed to classify different entropy functionals.

Purpose of the Study:

  • To provide an abstract, unified framework for classifying entropy functionals.
  • To explore the role of non-interacting systems and extensivity in entropy classification.
  • To establish a systematic method for understanding the merits of various entropy forms.

Main Methods:

  • Defining entropy as a functional on a probability space.
  • Analyzing the properties of non-interacting systems within this abstract framework.
  • Investigating the requirement of extensivity for entropy classification.

Main Results:

  • A systematic classification of entropy functional forms is achievable.
  • The handling of trivial cases (non-interacting systems) is crucial for classification.
  • Extensivity emerges as a key requirement for this systematic approach.

Conclusions:

  • The abstract functional approach, considering non-interacting systems and extensivity, offers a powerful method for classifying entropy.
  • This framework clarifies the importance and merits of different entropy measures.
  • It provides a unified perspective on entropy across various scientific disciplines.