Information entropy, information distances, and complexity in atoms

Chatzisavvas, K. Ch.; Moustakidis, Ch. C.; Panos, C. P.

doi:10.1063/1.2121610

Cited by 165 publications

(75 citation statements)

References 39 publications

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“…To underline the difference between the quantum entropy and information energy, let us consider a simple example that justifies the study of the latter; namely, it is easy to show [69,70] that for the discrete field with N events the information energy (entropy) reaches minimum of 1/N (maximum of ln N ) when the likelihoods of all occurences are equal while the unit maximum (zero minimum) takes place with the probability of one event being certain with all others turning to zeros. Since the former case corresponds to a complete disorder, by analogy with thermodynamics the quantity O is coined as 'energy' though actually it is measured in units of the inverse volume of the field upon which it is calculated.…”

Section: Introductionmentioning

confidence: 99%

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Theory of the Robin quantum wall in a linear potential. I. Energy spectrum, polarization and quantum‐information measures

Olendski

2016

Annalen der Physik

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Information-theoretical concepts are employed for the analysis of the interplay between a transverse electric field E applied to a one-dimensional surface and Robin boundary condition (BC), which with the help of the extrapolation length Λ zeroes at the interface a linear combination of the quantum mechanical wave function and its spatial derivative, and its influence on the properties of the structure. For doing this, exact analytical solutions of the corresponding Schrödinger equation are derived and used for calculating energies, dipole moments, position Sx and momentum S k quantum information entropies and their Fisher information Ix and I k and Onicescu information energies Ox and O k counterparts. It is shown that the weak (strong) electric field changes the Robin wall into the Dirichlet, Λ = 0 (Neumann, Λ = ∞), surface. This transformation of the energy spectrum and associated waveforms in the growing field defines an evolution of the quantum-information measures; for example, it is proved that for the Dirichlet and Neumann BCs the position (momentum) quantum information entropy varies as a positive (negative) natural logarithm of the electric intensity what results in their field-independent sum Sx + S k . Analogously, at Λ = 0 and Λ = ∞ the position and momentum Fisher informations (Onicescu energies) depend on the applied voltage as E 2/3 (E 1/3 ) and its inverse, respectively, leading to the field-independent product IxI k (OxO k ). Peculiarities of their transformations at the finite nonzero Λ are discussed and similarities and differences between the three quantum-information measures in the electric field are highlighted with the special attention being paid to the configuration with the negative extrapolation length.

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Section: Introductionmentioning

confidence: 99%

“…Similar to the quantum entropy and Fisher information, it finds applications not only in physics but, for example, in social sciences [71]. A comparison of the three information measures has been performed for a number of systems [40,[69][70][71][72]. For the only bound state of the negative Robin wall the information energies are:…”

Section: Introductionmentioning

confidence: 99%

Theory of the Robin quantum wall in a linear potential. I. Energy spectrum, polarization and quantum‐information measures

Olendski

2016

Annalen der Physik

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“…Using different phase-spaces to measure Shannon entropy will lead to different expressions. Studies of Shannon entropy in position space and momentum space of atomic systems have been carried out [7][8][9][10][11][12][13][14]. We calculate Shannon entropy in position basis and momentum basis to discuss the correlation.…”

Section: Open Accessmentioning

confidence: 99%

Statistical Correlations of the N-particle Moshinsky Model

Peng

2015

Entropy

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Abstract:We study the correlation of the ground state of an N-particle Moshinsky model by computing the Shannon entropy in both position and momentum spaces. We have derived the Shannon entropy and mutual information with analytical forms of such an N-particle Moshinsky model, and this helps us test the entropic uncertainty principle. The Shannon entropy in position space decreases as interaction strength increases. However, Shannon entropy in momentum space has the opposite trend. Shannon entropy of the whole system satisfies the equality of entropic uncertainty principle. Our results also indicate that, independent of the sizes of the two subsystems, the mutual information increases monotonically as the interaction strength increases.

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“…In [61] the Jensen-Shannon distribution was first proposed as a measure of distinguishability of two quantum states. Chatzisavvas et al investigated the quantity for atomic density functions [62].…”

Section: Kullback-leibler Missing Informationmentioning

confidence: 99%

Atomic Density Functions: Atomic Physics Calculations Analyzed with Methods from Quantum Chemistry

Borgoo

Godefroid

Geerlings

2011

Advances in the Theory of Quantum Systems in Chemistry and Physics

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This contribution reviews a selection of findings on atomic density functions and discusses ways for reading chemical information from them. First an expression for the density function for atoms in the multi-configuration Hartree-Fock scheme is established. The spherical harmonic content of the density function and ways to restore the spherical symmetry in a general open-shell case are treated. The evaluation of the density function is illustrated in a few examples. In the second part of the paper, atomic density functions are analyzed using quantum similarity measures. The comparison of atomic density functions is shown to be useful to obtain physical and chemical information. Finally, concepts from information theory are introduced and adopted for the comparison of density functions. In particular, based on the Kullback-Leibler form, a functional is constructed that reveals the periodicity in Mendeleev's table. Finally a quantum similarity measure is constructed, based on the integrand of the Kullback-Leibler expression and the periodicity is regained in a different way.

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Information entropy, information distances, and complexity in atoms

Cited by 165 publications

References 39 publications

Theory of the Robin quantum wall in a linear potential. I. Energy spectrum, polarization and quantum‐information measures

Theory of the Robin quantum wall in a linear potential. I. Energy spectrum, polarization and quantum‐information measures

Statistical Correlations of the N-particle Moshinsky Model

Atomic Density Functions: Atomic Physics Calculations Analyzed with Methods from Quantum Chemistry

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