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14 pages, 2357 KiB

Open AccessArticle

Global Quantum Information-Theoretic Measures in the Presence of Magnetic and Aharanov-Bohm (AB) Fields

by Collins Okon Edet, Emmanuel Benjamin Ettah, Syed Alwee Aljunid, Rosdisham Endut, Norshamsuri Ali, Akpan Ndem Ikot and Muhammad Asjad

Symmetry 2022, 14(5), 976; https://doi.org/10.3390/sym14050976 - 10 May 2022

Cited by 15 | Viewed by 2160

Abstract

The global quantum information-theoretical analysis of the class of Yukawa potential (CYP) in the presence of magnetic and Aharonov–Bohm (AB) fields has been examined both analytically and numerically in this research piece. The energy equation and wave function for the CYP are obtained by solving the Schrodinger equation in the presence of external magnetic and AB fields using the functional analysis technique. The probability density is used to calculate the Tsallis, Rényi, and Onicescu information energy entropies numerically. The influence of the screening parameter

(β)

, magnetic

(\vec{B})

, and AB

(ξ)

fields on the global information-theoretical measurements for the CYP is explored. Atomic and molecular physics, quantum chemistry, and physics are specific areas where these research findings will find application. Full article

(This article belongs to the Special Issue Quantum Mechanics: Concepts, Symmetries, and Recent Developments)

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15 pages, 401 KiB

Open AccessArticle

Onicescu’s Informational Energy and Correlation Coefficient in Exponential Families

by Frank Nielsen

Foundations 2022, 2(2), 362-376; https://doi.org/10.3390/foundations2020025 - 19 Apr 2022

Cited by 4 | Viewed by 5517

Abstract

The informational energy of Onicescu is a positive quantity that measures the amount of uncertainty of a random variable. However, contrary to Shannon’s entropy, the informational energy is strictly convex and increases when randomness decreases. We report a closed-form formula for Onicescu’s informational energy and its associated correlation coefficient when the probability distributions belong to an exponential family. We show how to instantiate the generic formula for several common exponential families. Finally, we discuss the characterization of valid thermodynamic process trajectories on a statistical manifold by enforcing that the entropy and the informational energy shall vary in opposite directions. Full article

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15 pages, 1104 KiB

Open AccessArticle

Shannon, Rényi, Tsallis Entropies and Onicescu Information Energy for Low-Lying Singly Excited States of Helium

by Jen-Hao Ou and Yew Kam Ho

Atoms 2019, 7(3), 70; https://doi.org/10.3390/atoms7030070 - 18 Jul 2019

Cited by 28 | Viewed by 4350

Abstract

Knowledge of the electronic structures of atomic and molecular systems deepens our understanding of the desired system. In particular, several information-theoretic quantities, such as Shannon entropy, have been applied to quantify the extent of electron delocalization for the ground state of various systems. [...] Read more.

α

and Tsallis entropy of order

α

, and Onicescu Information Energy of order

α

for four low-lying singly excited states (1s2s

^{1} S^{e}

, 1s2s

^{3} S^{e}

, 1s3s

^{1} S^{e}

, and 1s3s

^{3} S^{e}

states) of helium. This paper compares the behavior of these three quantities of order 0.5 to 9 for the ground and four excited states. We found that, generally, a higher excited state had a larger Rényi entropy, larger Tsallis entropy, and smaller Onicescu information energy. However, this trend was not definite and the singlet–triplet reversal occurred for Rényi entropy, Tsallis entropy and Onicescu information energy at a certain range of order

α

. Full article

(This article belongs to the Section Quantum Chemistry, Computational Chemistry and Molecular Physics)

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12 pages, 1250 KiB

Open AccessArticle

Transfer Information Energy: A Quantitative Indicator of Information Transfer between Time Series

by Angel Caţaron and Răzvan Andonie

Entropy 2018, 20(5), 323; https://doi.org/10.3390/e20050323 - 27 Apr 2018

Cited by 9 | Viewed by 4610

Abstract

We introduce an information-theoretical approach for analyzing information transfer between time series. Rather than using the Transfer Entropy (TE), we define and apply the Transfer Information Energy (TIE), which is based on Onicescu’s Information Energy. Whereas the TE can be used as a measure of the reduction in uncertainty about one time series given another, the TIE may be viewed as a measure of the increase in certainty about one time series given another. We compare the TIE and the TE in two known time series prediction applications. First, we analyze stock market indexes from the Americas, Asia/Pacific and Europe, with the goal to infer the information transfer between them (i.e., how they influence each other). In the second application, we take a bivariate time series of the breath rate and instantaneous heart rate of a sleeping human suffering from sleep apnea, with the goal to determine the information transfer heart → breath vs. breath → heart. In both applications, the computed TE and TIE values are strongly correlated, meaning that the TIE can substitute the TE for such applications, even if they measure symmetric phenomena. The advantage of using the TIE is computational: we can obtain similar results, but faster. Full article

(This article belongs to the Special Issue Selected Papers from the 26th International Conference on Artificial Neural Networks - ICANN 2017)

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