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Entropy02:39

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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...
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A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
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On eccentricity-based entropy measures for dendrimers.

Rongbing Huang1, Muhammad Kamran Siddiqui2, Shazia Manzoor2

  • 1School of Computer Science Chengdu University, Chengdu, China.

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|August 30, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces eccentricity-based entropy for analyzing complex networks and radical dendrimers. Eccentricity-based indices and entropies were computed for cyclotriphosphazene dendrimers, showing their potential in biomedical applications.

Keywords:
Cyclotriphosphazene-based dendrimerEccentricity-based indicesEntropyMolecular graph

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Area of Science:

  • Information theory
  • Materials science
  • Biomedical engineering

Background:

  • Shannon's entropy quantifies structural information in complex networks.
  • Radical dendrimers show promise in biomedical applications like anti-tumor agents and MRI.
  • Cyclotriphosphazene dendrimers offer unique structural properties for advanced applications.

Purpose of the Study:

  • To compute eccentricity-based indices and entropies for cyclotriphosphazene dendrimers.
  • To explore the relationship between these indices and their corresponding entropies.
  • To assess the potential of these dendrimers in biomedical and materials science fields.

Main Methods:

  • Calculation of eccentricity-based indices for dendrimer structures.
  • Development of eccentricity-based entropies derived from these indices.
  • Analysis of electron paramagnetic resonance (EPR) temperature spectrum for characterization.

Main Results:

  • Numerical and graphical representation of computed eccentricity-based indices and entropies.
  • Demonstration of a correlation between dendrimer structure and information-theoretic properties.
  • Validation of cyclotriphosphazene dendrimers' suitability for advanced applications.

Conclusions:

  • Eccentricity-based entropy provides a valuable tool for understanding complex network structures, including dendrimers.
  • The study highlights the significance of cyclotriphosphazene dendrimers in advanced materials and biomedical fields.
  • The findings support the development of new devices based on the paramagnetic properties of organic radicals.