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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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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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Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.
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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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Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
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Low-algorithmic-complexity entropy-deceiving graphs.

Hector Zenil1, Narsis A Kiani2, Jesper Tegnér3

  • 1Information Dynamics Lab, Unit of Computational Medicine, Department of Medicine Solna, Center for Molecular Medicine, SciLifeLab, Karolinska Institute, Stockholm 171 76, Sweden; Department of Computer Science, University of Oxford, Oxford OX1 3QD, United Kingdom; and Algorithmic Nature Group, LABoRES, Paris 75006, France.

Physical Review. E
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Summary
This summary is machine-generated.

Graph complexity measures can be misleading. Computable measures like Shannon entropy may misrepresent a graph

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Area of Science:

  • Graph theory
  • Information theory
  • Computational complexity

Background:

  • Estimating object complexity often relies on graph- and information-theoretic measures.
  • Existing measures may be dependent on the object's description or observation method.

Purpose of the Study:

  • To investigate the independence of graph complexity measures from descriptive methods.
  • To demonstrate how computable measures can misrepresent graph properties.
  • To explore the limitations of computable complexity measures.

Main Methods:

  • Utilized integer sequences with properties like Borel normality for graph construction.
  • Introduced recursive and nonrecursive (uncomputable) graphs.
  • Analyzed disparate entropy values from different lossless descriptions of the same graph.

Main Results:

  • Graph complexity measures are not independent of how the object is described or observed.
  • Computable measures like Shannon entropy require arbitrary selections and can misrepresent causal likelihood.
  • Different lossless descriptions of the same graph yield disparate entropy values.

Conclusions:

  • Computable measures of complexity, such as entropy, have significant weaknesses.
  • The choice of description significantly impacts complexity estimations.
  • Further exploration of measure applications and limitations is warranted.