Relative Rényi entropy for atoms

Nagy, Á.; Romera, E.

doi:10.1002/qua.21962

Cited by 36 publications

(25 citation statements)

References 60 publications

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“…The explicit evaluation of the Rényi entropy, Tsallis entropy, and Onicescu information energy for the SCP shall be shown in this section. The Rényi entropy from Equation is expressed as

R_{q}^{SCP} true[{normalρ}_{n} true] = \frac{1}{1 - q} \ln W_{q}^{SCP} true[{normalρ}_{n} true],

where the entropic moment

W_{q}^{SCP} true[{normalρ}_{n} true]

is expressed as

W_{q}^{SCP} true[{normalρ}_{n} true] = \int_{0}^{\infty} {[normalρ false(r false)]}^{q} d r = \frac{N_{n l}^{2 q}}{4 a} \int_{- 1}^{1} {(\frac{1 - z}{2})}^{2 ϵ q - 1} {true(\frac{1 + z}{2} true)}^{2 ℓ q + 2 q} {true[P_{n}^{(2 ϵ, 2 ℓ + 1)} (z) true]}^{2 q} d z, z = 1 - 2 s .

…”

Section: Information‐theoretic Measures For the Scpmentioning

confidence: 99%

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Quantum information‐theoretic measures for the static screened Coulomb potential

Isonguyo

Oyewumi

Oyun

2018

Int J of Quantum Chemistry

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In this research work, the quantum information‐theoretic analysis of the static screened Coulomb potential has been carried out by studying both analytically and numerically the entropic measures, Fisher information as well as the Onicescu information energy of its wave function. Explicit expressions of these information‐theoretic measures were obtained. Using the Srivastava–Daoust linearization formula in terms of the multivariate Lauricella hypergeometric function, the Rényi entropy, Tsallis entropy, Onicescu information energy were analytically obtained. From the results obtained, it is observed that some of the Shannon entropies are negative, indicating that, negative entropies exists for the probability densities that are highly localized. The trends in the variation of the information‐theoretic measures with the potential screening parameter a for this atomic model are discussed. The Bialynicki‐Birula, Mycielski inequality (BBM), and the Fisher information based uncertainty relation are also verified.

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“…The explicit evaluation of the Rényi entropy, Tsallis entropy, and Onicescu information energy for the SCP shall be shown in this section. The Rényi entropy from Equation is expressed as

R_{q}^{SCP} true[{normalρ}_{n} true] = \frac{1}{1 - q} \ln W_{q}^{SCP} true[{normalρ}_{n} true],

where the entropic moment

W_{q}^{SCP} true[{normalρ}_{n} true]

is expressed as

W_{q}^{SCP} true[{normalρ}_{n} true] = \int_{0}^{\infty} {[normalρ false(r false)]}^{q} d r = \frac{N_{n l}^{2 q}}{4 a} \int_{- 1}^{1} {(\frac{1 - z}{2})}^{2 ϵ q - 1} {true(\frac{1 + z}{2} true)}^{2 ℓ q + 2 q} {true[P_{n}^{(2 ϵ, 2 ℓ + 1)} (z) true]}^{2 q} d z, z = 1 - 2 s .

…”

Section: Information‐theoretic Measures For the Scpmentioning

confidence: 99%

“…Figures 4A,B and 5A The explicit evaluation of the R enyi entropy, Tsallis entropy, and Onicescu information energy for the SCP shall be shown in this section. The R enyi entropy from Equation 4 is expressed as [2,51]…”

Section: N F Orm a Ti On -The Or Eti C M Ea S U R Es F Or Th E S Cpmentioning

confidence: 99%

Quantum information‐theoretic measures for the static screened Coulomb potential

Isonguyo

Oyewumi

Oyun

2018

Int J of Quantum Chemistry

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“…KL has also been used in molecular dynamics simulations . Relative information, based on other measures such as Fisher information, or Rényi entropy, has also been examined in varied contexts.…”

Section: Introductionmentioning

confidence: 99%

Entropic Kullback‐Leibler type distance measures for quantum distributions

Laguna

Salazar

Sagar

2019

Int J of Quantum Chemistry

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Entropic distance measures for quantum mechanical probability distributions, which are characterized by nodal structure and symmetry holes, are considered. We illustrate how the Kullback-Leibler (KL) distance is not well defined in some instances and propose instead the use of the cumulative residual Kullback-Leibler (CRKL) distance.The KL and CRKL measures are compared and contrasted for some representative quantum mechanical systems: The particle in an infinite well, the harmonic oscillator, and hydrogenic systems. We present cases where CRKL can be used to obtain distances whereas KL cannot be used, and also highlight examples where the KL and CRKL measures yield different behaviors and interpretations. An extension of the CRKL definition is obtained for application to harmonic oscillator systems defined over [−∞, ∞]. Distance measures for two-variable (particle) distributions are also considered to address generalizations of the mutual information correlation measure.The use of CRKL in measuring distances between orbitals is also discussed. K E Y W O R D S cumulative residual Kullback-Leibler entropy, Kullback-Leibler, quantum distributions, relative entropy

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“…Relative R and S was studied for various atomic systems using H atom ground state as reference [36]. A detailed exploration reveals that, they are directly connected with atomic radii and quantum capacitance [36,37].…”

Section: Introductionmentioning

confidence: 99%

Relative Fisher information in some central potentials

Mukherjee

Roy

2018

Annals of Physics

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Relative Fisher information (IR), which is a measure of correlative fluctuation between two probability densities, has been pursued for a number of quantum systems, such as, 1D quantum harmonic oscillator (QHO) and a few central potentials namely, 3D isotropic QHO, hydrogen atom and pseudoharmonic potential (PHP) in both position (r) and momentum (p) spaces. In the 1D case, the n = 0 state is chosen as reference, whereas for a central potential, the respective circular or node-less (corresponding to lowest radial quantum number n r ) state of a given l quantum number, is selected. Starting from their exact wave functions, expressions of IR in both r and p spaces are obtained in closed analytical forms in all these systems. A careful analysis reveals that, for the 1D QHO, IR in both coordinate spaces increase linearly with quantum number n. Likewise, for 3D QHO and PHP, it varies with single power of radial quantum number n r in both spaces. But, in H atom they depend on both principal (n) and azimuthal (l) quantum numbers. However, at a fixed l, IR (in conjugate spaces) initially advance with rise of n and then falls off; also for a given n, it always decreases with l.

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Relative Rényi entropy for atoms

Cited by 36 publications

References 60 publications

Quantum information‐theoretic measures for the static screened Coulomb potential

Quantum information‐theoretic measures for the static screened Coulomb potential

Entropic Kullback‐Leibler type distance measures for quantum distributions

Relative Fisher information in some central potentials

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