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Entropy02:39

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...
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The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
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The process of surrounding a solute with solvent is called solvation. It involves evenly distributing the solute within the solvent. The rule of thumb for determining a solvent for a given compound is that like dissolves like. A good solvent has molecular characteristics similar to those of the compound to be dissolved. For example, polar solutions dissolve polar solutes, and apolar solvents dissolve apolar solutes. A polar solvent is a solvent that has a high dielectric constant (ϵ...
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A living cell's primary tasks of obtaining, transforming, and using energy to do work may seem simple. However, the second law of thermodynamics explains why these tasks are harder than they appear. None of the energy transfers in the universe are completely efficient. In every energy transfer, some amount of energy is lost in a form that is unusable. In most cases, this form is heat energy. Thermodynamically, heat energy is defined as the energy transferred from one system to another that...
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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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Modeling the Functional Network for Spatial Navigation in the Human Brain
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Entropy of spatial network ensembles.

Justin P Coon1, Carl P Dettmann2, Orestis Georgiou2,3

  • 1Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, United Kingdom.

Physical Review. E
|May 16, 2018
PubMed
Summary
This summary is machine-generated.

We introduce a new framework using graph entropy to analyze spatial networks. This research reveals that real-world networks like wireless and flight systems approach maximum entropy, suggesting efficient information organization.

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Area of Science:

  • Network Science
  • Information Theory
  • Statistical Physics

Background:

  • Spatial networks are fundamental to many systems.
  • Understanding their complexity is crucial for optimization.
  • Existing models often simplify the inherent randomness.

Purpose of the Study:

  • To develop a mathematical framework for analyzing spatial network ensembles using graph entropy.
  • To investigate the relationship between node distribution, connection functions, and network entropy.
  • To determine the connection function that maximizes entropy under given constraints.

Main Methods:

  • Modeling spatial networks as soft random geometric graphs with dual randomness (node positions and link formation).
  • Deriving analytical bounds for the entropy of spatial network ensembles.
  • Calculating conditional entropy for hard and soft pair connection functions.
  • Applying the framework to real-world networks like ad hoc wireless and US flight networks.

Main Results:

  • A general formalism for analyzing spatial network ensembles via graph entropy is established.
  • Simple entropy bounds and conditional entropy calculations are derived.
  • The connection function yielding maximum entropy under general constraints is identified.
  • Ad hoc wireless and US flight networks demonstrate properties of nearly maximally entropic ensembles.

Conclusions:

  • The developed framework provides a robust method for quantifying spatial network complexity.
  • Real-world networks exhibit near-maximal entropy, indicating efficient structural properties.
  • This approach offers insights into network design and optimization for improved performance.