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Related Concept Videos

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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Entropy and the Second Law of Thermodynamics01:20

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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.
The relation  between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
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The Second Law of Thermodynamics01:14

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In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be...
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One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

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This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
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Third Law of Thermodynamics02:38

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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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Standard Entropy Change for a Reaction03:00

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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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Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
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On Generalized Schürmann Entropy Estimators.

Peter Grassberger1

  • 1Jülich Supercomputing Center, Jülich Research Center, D-52425 Jülich, Germany.

Entropy (Basel, Switzerland)
|May 28, 2022
PubMed
Summary
This summary is machine-generated.

We developed novel Shannon entropy estimators for undersampled discrete distributions. These estimators are unbiased with finite variance, challenging prior assumptions in statistical estimation.

Keywords:
Bayesianbiasentropy estimatesmutual information estimatesundersamplingvariance

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Area of Science:

  • Information Theory
  • Statistical Estimation

Background:

  • Estimating Shannon entropy for discrete distributions is challenging, especially with limited data.
  • Existing methods often struggle with bias and variance issues in undersampled scenarios.

Purpose of the Study:

  • To introduce a new class of Shannon entropy estimators.
  • To address the limitations of current estimators in severely undersampled discrete distributions.

Main Methods:

  • Generalizing previously proposed entropy estimators.
  • Developing estimators with specific parameter choices to achieve desired statistical properties.

Main Results:

  • The new estimators are unbiased and possess finite variance, even for severely undersampled distributions.
  • Numerical tests demonstrate superior performance compared to existing estimators and exact values.
  • A conflict with Bayesian estimators for mutual information was identified.

Conclusions:

  • The proposed estimators offer a significant advancement in accurately quantifying Shannon entropy from sparse data.
  • These findings challenge conventional understanding regarding bias and variance in entropy estimation.