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Related Concept Videos

Quantum Numbers02:43

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
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When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...
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The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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Ludwig Edward Boltzmann developed a definition for entropy, which stated that absolute entropy is proportional to the natural logarithm of the number of possible combinations of particles. Entropy stands alone among state functions as the only one whose absolute values can be determined.Consider a gas sample confined to a container. As the container expands, the energy levels of gas molecules become more closely spaced. This increases the number of available energy states, thereby increasing...
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The first law of thermodynamics establishes that the change in internal energy of a system is given by ΔU = q + w, where q is the heat exchanged, and w is the work performed. For a perfect gas, both internal energy (U) and enthalpy (H) depend solely on temperature. Consequently, for any change of state, whether reversible or irreversible, the internal energy change is determined by integrating the heat capacity at constant volume, and the enthalpy change by integrating the heat capacity at...

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Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy
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Correction: Naudts, J. Quantum Statistical Manifolds. Entropy 2018, 20, 472.

Jan Naudts1

  • 1Departement Fysica, Universiteit Antwerpen, Universiteitsplein 1, 2610 Wilrijk Antwerpen, Belgium.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary

This paper corrects errors in Section 4 and Theorem 3 of "Quantum Statistical Manifolds," improving the accuracy of quantum statistical manifold research. A revised section and additional references enhance the original work.

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Area of Science:

  • Quantum Information Theory
  • Statistical Mechanics
  • Differential Geometry

Context:

  • The original paper introduced quantum statistical manifolds.
  • Errors were identified in Section 4 and Theorem 3 of the published work.
  • These errors had minor implications for the broader conclusions.

Purpose:

  • To provide a corrected version of Section 4.
  • To amend the incomplete proof of Theorem 3.
  • To address minor shortcomings and add missing references.

Summary:

  • A revised Section 4 is presented, rectifying identified errors.
  • The proof for Theorem 3 has been completed and is now accurate.
  • Several minor issues within the paper have been resolved, including the addition of omitted references.

Impact:

  • Ensures the reliability and accuracy of research on quantum statistical manifolds.
  • Provides a more robust foundation for future studies in the field.
  • Enhances the overall quality and completeness of the original publication.