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Roy R, Chakrabarti B, Chavda ND, Lekala ML. Information theoretic measures for interacting bosons in optical lattice. Phys Rev E 2023; 107:024119. [PMID: 36932481 DOI: 10.1103/physreve.107.024119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2022] [Accepted: 01/19/2023] [Indexed: 06/18/2023]
Abstract
This work reports the different information theoretic measures, i.e., Shannon information entropy, order, disorder, complexity, and their dynamical measure for the interacting bosons in an optical lattice with both commensurate and incommensurate filling factor. We solve the many-body Schrödinger equation from first principles by multiconfigurational time-dependent Hartree method which calculates all the measures with high level of accuracy. We find for both relaxed state as well as quenched state the López-Ruiz-Mancini-Calbet (LMC) measure of complexity is the most efficient depictor of superfluid (SF) to Mott-insulator transition. In the quench dynamics, the distinct structure of LMC complexity can be used as a "figure of merit" to obtain the timescale of SF to Mott state entry, Mott holding time, and the Mott state to SF state entry in the successive cycles. We also find that fluctuations in the dynamics of LMC complexity measure for incommensurate filling clearly establish that superfluid to Mott-insulator transition is incomplete. We overall conclude that distinct structure in the complexity makes it more sensitive than the standard use of Shannon information entropy.
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Affiliation(s)
- Rhombik Roy
- Department of Physics, Presidency University, 86/1 College Street, Kolkata 700073, India
| | - Barnali Chakrabarti
- Department of Physics, Presidency University, 86/1 College Street, Kolkata 700073, India
| | - N D Chavda
- Department of Applied Physics, Faculty of Technology and Engineering, The Maharaja Sayajirao University of Baroda, Vadodara-390001, India
| | - M L Lekala
- Department of Physics, University of South Africa, P.O. Box 392, Pretoria 0003, South Africa
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α-Geodesical Skew Divergence. ENTROPY 2021; 23:e23050528. [PMID: 33923103 PMCID: PMC8146191 DOI: 10.3390/e23050528] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/01/2021] [Revised: 04/22/2021] [Accepted: 04/24/2021] [Indexed: 01/25/2023]
Abstract
The asymmetric skew divergence smooths one of the distributions by mixing it, to a degree determined by the parameter λ, with the other distribution. Such divergence is an approximation of the KL divergence that does not require the target distribution to be absolutely continuous with respect to the source distribution. In this paper, an information geometric generalization of the skew divergence called the α-geodesical skew divergence is proposed, and its properties are studied.
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Abstract
This paper presents a quantitative approach to poetry, based on the use of several statistical measures (entropy, informational energy, N-gram, etc.) applied to a few characteristic English writings. We found that English language changes its entropy as time passes, and that entropy depends on the language used and on the author. In order to compare two similar texts, we were able to introduce a statistical method to asses the information entropy between two texts. We also introduced a method of computing the average information conveyed by a group of letters about the next letter in the text. We found a formula for computing the Shannon language entropy and we introduced the concept of N-gram informational energy of a poetry. We also constructed a neural network, which is able to generate Byron-type poetry and to analyze the information proximity to the genuine Byron poetry.
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Statistics and Machine Learning Experiments in English and Romanian Poetry. SCI 2020. [DOI: 10.3390/sci2040078] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
This paper presents a quantitative approach to poetry, based on the use of several statistical measures (entropy, informational energy, N-gram, etc.) applied to a few characteristic English writings. We found that English language changes its entropy as time passes, and that entropy depends on the language used and on the author. In order to compare two similar texts, we were able to introduce a statistical method to asses the information entropy between two texts. We also introduced a method of computing the average information conveyed by a group of letters about the next letter in the text. We found a formula for computing the Shannon language entropy and we introduced the concept of N-gram informational energy of a poetry. We also constructed a neural network, which is able to generate Byron-type poetry and to analyze the information proximity to the genuine Byron poetry.
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Hazra S. A comparative study on information theoretic approach for atomic and molecular systems. COMPUT THEOR CHEM 2020. [DOI: 10.1016/j.comptc.2020.112801] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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On a Generalization of the Jensen-Shannon Divergence and the Jensen-Shannon Centroid. ENTROPY 2020; 22:e22020221. [PMID: 33285995 PMCID: PMC7516653 DOI: 10.3390/e22020221] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/05/2019] [Revised: 02/14/2020] [Accepted: 02/14/2020] [Indexed: 11/16/2022]
Abstract
The Jensen–Shannon divergence is a renown bounded symmetrization of the Kullback–Leibler divergence which does not require probability densities to have matching supports. In this paper, we introduce a vector-skew generalization of the scalar α-Jensen–Bregman divergences and derive thereof the vector-skew α-Jensen–Shannon divergences. We prove that the vector-skew α-Jensen–Shannon divergences are f-divergences and study the properties of these novel divergences. Finally, we report an iterative algorithm to numerically compute the Jensen–Shannon-type centroids for a set of probability densities belonging to a mixture family: This includes the case of the Jensen–Shannon centroid of a set of categorical distributions or normalized histograms.
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Rong C, Wang B, Zhao D, Liu S. Information‐theoretic approach in density functional theory and its recent applications to chemical problems. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2019. [DOI: 10.1002/wcms.1461] [Citation(s) in RCA: 29] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Chunying Rong
- Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research (Ministry of Education of China) Hunan Normal University Changsha P.R. China
- Department of Chemistry, College of Chemistry and Chemical Engineering Hunan Normal University Changsha P.R. China
| | - Bin Wang
- Department of Chemistry, College of Chemistry and Chemical Engineering Hunan Normal University Changsha P.R. China
| | - Dongbo Zhao
- Department of Chemistry, School of Chemistry and Chemical Engineering Nanjing University Nanjing P.R. China
| | - Shubin Liu
- Research Computing Centre University of North Carolina Chapel Hill North Carolina
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Shannon, Rényi, Tsallis Entropies and Onicescu Information Energy for Low-Lying Singly Excited States of Helium. ATOMS 2019. [DOI: 10.3390/atoms7030070] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
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. To explore excited states, we calculated Shannon entropy and two of its one-parameter generalizations, Rényi entropy of order 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 .
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11
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Link between generalized nonidempotency and complexity measures. J Mol Model 2017; 23:159. [PMID: 28405847 DOI: 10.1007/s00894-017-3331-y] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2016] [Accepted: 03/27/2017] [Indexed: 10/19/2022]
Abstract
The nonidempotency measure of Löwdin is found to be proportional to the disequilibrium. It is shown that there exists a simple relationship between the LMC (López-Ruiz-Mancini-Calbet) and the generalized statistical complexities and the generalized nonidempotency measure of Löwdin. Results are illustrated for an exactly solvable two-electron model atom.
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Esquivel RO, Molina-Espíritu M, López-Rosa S, Soriano-Correa C, Barrientos-Salcedo C, Kohout M, Dehesa JS. Predominant information quality scheme for the essential amino acids: an information-theoretical analysis. Chemphyschem 2015; 16:2571-81. [PMID: 26175003 DOI: 10.1002/cphc.201500282] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2015] [Revised: 05/11/2015] [Indexed: 11/05/2022]
Abstract
In this work we undertake a pioneer information-theoretical analysis of 18 selected amino acids extracted from a natural protein, bacteriorhodopsin (1C3W). The conformational structures of each amino acid are analyzed by use of various quantum chemistry methodologies at high levels of theory: HF, M062X and CISD(Full). The Shannon entropy, Fisher information and disequilibrium are determined to grasp the spatial spreading features of delocalizability, order and uniformity of the optimized structures. These three entropic measures uniquely characterize all amino acids through a predominant information-theoretic quality scheme (PIQS), which gathers all chemical families by means of three major spreading features: delocalization, narrowness and uniformity. This scheme recognizes four major chemical families: aliphatic (delocalized), aromatic (delocalized), electro-attractive (narrowed) and tiny (uniform). All chemical families recognized by the existing energy-based classifications are embraced by this entropic scheme. Finally, novel chemical patterns are shown in the information planes associated with the PIQS entropic measures.
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Affiliation(s)
- Rodolfo O Esquivel
- Departamento de Química, Universidad Autónoma Metropolitana, 09340-México, D.F. (México). .,Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada (Spain).
| | | | - Sheila López-Rosa
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada (Spain).,Departamento de Física Aplicada II, Universidad de Sevilla, 41012-Sevilla (Spain)
| | - Catalina Soriano-Correa
- Laboratorio de Química Computacional, FES-Zaragoza, Universidad Nacional Autónoma de México, 09230-Iztapalapa, México, D.F. (México)
| | - Carolina Barrientos-Salcedo
- Facultad de Bioanálisis-Veracruz, Universidad Veracruzana, Laboratorio de Química Médica y Quimiogenómica, 91700-Veracruz (México)
| | - Miroslav Kohout
- Max Planck Institute for Chemical Physics of Solids, Noethnitzer Str. 40, 01187-Dresden (Germany)
| | - Jesús S Dehesa
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada (Spain)
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Martín A, López-Rosa S, Angulo J, Antolín J. Jensen–Shannon and Kullback–Leibler divergences as quantifiers of relativistic effects in neutral atoms. Chem Phys Lett 2015. [DOI: 10.1016/j.cplett.2015.06.037] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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14
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Lin CH, Ho YK. Shannon information entropy in position space for two-electron atomic systems. Chem Phys Lett 2015. [DOI: 10.1016/j.cplett.2015.05.029] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Romera E, Calixto M, Nagy Á. Complexity measure and quantum shape-phase transitions in the two-dimensional limit of the vibron model. J Mol Model 2014; 20:2237. [PMID: 24948526 DOI: 10.1007/s00894-014-2237-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2014] [Accepted: 04/07/2014] [Indexed: 11/24/2022]
Abstract
We obtain a characterization of quantum shape-phase transitions in the terms of complexity measures in the two-dimensional limit of the vibron model based on the spectrum generating algebra U(3). Complexity measures (in terms of the Rényi entropies) have been calculated for different values of the control parameter for the ground state of this model giving sharp signatures of the quantum shape-phase transition from linear to bent molecules.
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Affiliation(s)
- Elvira Romera
- Instituto Carlos I de Fisica Teorica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071, Granada, Spain,
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Controlling the shannon entropy of quantum systems. THESCIENTIFICWORLDJOURNAL 2013; 2013:381219. [PMID: 23818819 PMCID: PMC3683499 DOI: 10.1155/2013/381219] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/10/2013] [Accepted: 04/26/2013] [Indexed: 11/17/2022]
Abstract
This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking.
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Concurrent Phenomena at the Reaction Path of the SN2 Reaction CH3Cl + F−. Information Planes and Statistical Complexity Analysis. ENTROPY 2013. [DOI: 10.3390/e15104084] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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Godó B, Nagy Á. Generalized complexity measures and chaotic maps. CHAOS (WOODBURY, N.Y.) 2012; 22:023118. [PMID: 22757525 DOI: 10.1063/1.4705088] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
The logistic and Tinkerbell maps are studied with the recently introduced generalized complexity measure. The generalized complexity detects periodic windows. Moreover, it recognizes the intersection of periodic branches of the bifurcation diagram. It also reflects the fractal character of the chaotic dynamics. There are cases where the complexity plot shows changes that cannot be seen in the bifurcation diagram.
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Affiliation(s)
- B Godó
- Department of Theoretical Physics, University of Debrecen, H-4010 Debrecen, Hungary
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22
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Alipour M, Mohajeri A. Onicescu information energy in terms of Shannon entropy and Fisher information densities. Mol Phys 2012. [DOI: 10.1080/00268976.2011.649795] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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Esquivel RO, Liu S, Angulo JC, Dehesa JS, Antolín J, Molina-Espíritu M. Fisher Information and Steric Effect: Study of the Internal Rotation Barrier of Ethane. J Phys Chem A 2011; 115:4406-15. [DOI: 10.1021/jp1095272] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Affiliation(s)
- Rodolfo O. Esquivel
- Departamento de Química, Universidad Autónoma Metropolitana, 09340 México D.F., México
| | - Shubin Liu
- Research Computing Center, University of North Carolina, Chapel Hill, North Carolina 27599-3420, United States
| | | | | | - Juan Antolín
- Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain
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Esquivel RO, Flores-Gallegos N, Dehesa JS, Angulo JC, Antolín J, López-Rosa S, Sen KD. Phenomenological Description of a Three-Center Insertion Reaction: An Information-Theoretic Study. J Phys Chem A 2010; 114:1906-16. [DOI: 10.1021/jp908898w] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Rodolfo O. Esquivel
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, 09340, México D.F., Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, and School of Chemistry, University of Hyderabad, Hyderabad 500046, India
| | - Nelson Flores-Gallegos
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, 09340, México D.F., Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, and School of Chemistry, University of Hyderabad, Hyderabad 500046, India
| | - Jesús S. Dehesa
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, 09340, México D.F., Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, and School of Chemistry, University of Hyderabad, Hyderabad 500046, India
| | - Juan Carlos Angulo
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, 09340, México D.F., Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, and School of Chemistry, University of Hyderabad, Hyderabad 500046, India
| | - Juan Antolín
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, 09340, México D.F., Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, and School of Chemistry, University of Hyderabad, Hyderabad 500046, India
| | - Sheila López-Rosa
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, 09340, México D.F., Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, and School of Chemistry, University of Hyderabad, Hyderabad 500046, India
| | - K. D. Sen
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, 09340, México D.F., Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, and School of Chemistry, University of Hyderabad, Hyderabad 500046, India
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Moustakidis CC, Psonis VP, Chatzisavvas KC, Panos CP, Massen SE. Statistical measure of complexity and correlated behavior of Fermi systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:011104. [PMID: 20365320 DOI: 10.1103/physreve.81.011104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2009] [Revised: 10/19/2009] [Indexed: 05/29/2023]
Abstract
We apply the statistical measure of complexity, introduced by López-Ruiz, Mancini, and Calbet (LMC), to uniform Fermi systems. We investigate the connection between information and complexity measures with the strongly correlated behavior of various Fermi systems as nuclear matter, electron gas, and liquid helium. We examine the possibility that LMC complexity can serve as an index quantifying correlations in the specific system and to which extent could be related with experimental quantities. Moreover, we concentrate on thermal effects on the complexity of ideal Fermi systems. We find that complexity behaves, both at low and high values of temperature, in a similar way as the specific heat.
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Affiliation(s)
- Ch C Moustakidis
- Department of Theoretical Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
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Esquivel RO, Angulo JC, Antolín J, Dehesa JS, López-Rosa S, Flores-Gallegos N. Analysis of complexity measures and information planes of selected molecules in position and momentum spaces. Phys Chem Chem Phys 2010; 12:7108-16. [DOI: 10.1039/b927055h] [Citation(s) in RCA: 57] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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López-Rosa S, Esquivel RO, Angulo JC, Antolín J, Dehesa JS, Flores-Gallegos N. Fisher Information Study in Position and Momentum Spaces for Elementary Chemical Reactions. J Chem Theory Comput 2009; 6:145-54. [DOI: 10.1021/ct900544m] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Affiliation(s)
- Sheila López-Rosa
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, Departamento de Química, Universidad Autónoma Metropolitana, 09340-México D.F., México, and Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain
| | - Rodolfo O. Esquivel
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, Departamento de Química, Universidad Autónoma Metropolitana, 09340-México D.F., México, and Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain
| | - Juan Carlos Angulo
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, Departamento de Química, Universidad Autónoma Metropolitana, 09340-México D.F., México, and Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain
| | - Juan Antolín
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, Departamento de Química, Universidad Autónoma Metropolitana, 09340-México D.F., México, and Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain
| | - Jesús S. Dehesa
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, Departamento de Química, Universidad Autónoma Metropolitana, 09340-México D.F., México, and Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain
| | - Nelson Flores-Gallegos
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, Departamento de Química, Universidad Autónoma Metropolitana, 09340-México D.F., México, and Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain
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Sagar RP, Laguna HG, Guevara NL. Conditional entropies and position–momentum correlations in atomic systems. Mol Phys 2009. [DOI: 10.1080/00268970903153675] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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31
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Esquivel RO, Flores-Gallegos N, Iuga C, Carrera EM, Angulo JC, Antolín J. Phenomenological description of the transition state, and the bond breaking and bond forming processes of selected elementary chemical reactions: an information-theoretic study. Theor Chem Acc 2009. [DOI: 10.1007/s00214-009-0641-x] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Shannon information entropy of fractional occupation probability as an electron correlation measure in atoms and molecules. Chem Phys 2009. [DOI: 10.1016/j.chemphys.2009.04.016] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Angulo JC, Antolín J. Atomic complexity measures in position and momentum spaces. J Chem Phys 2008; 128:164109. [DOI: 10.1063/1.2907743] [Citation(s) in RCA: 69] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Luzanov AV. Spectral and entropic characterizations of Wigner functions: Applications to model vibrational systems. J Chem Phys 2008; 129:094103. [DOI: 10.1063/1.2968607] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Borgoo A, De Proft F, Geerlings P, Sen K. Complexity of Dirac–Fock atom increases with atomic number. Chem Phys Lett 2007. [DOI: 10.1016/j.cplett.2007.07.003] [Citation(s) in RCA: 56] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Sagar RP, Guevara NL. Shannon entropies of atomic structure factors, off-diagonal order and radial correlation. Mol Phys 2007. [DOI: 10.1080/00268970701335771] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Sen KD, Katriel J. Information entropies for eigendensities of homogeneous potentials. J Chem Phys 2006; 125:074117. [PMID: 16942332 DOI: 10.1063/1.2263710] [Citation(s) in RCA: 52] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
For homogeneous potentials, the sum S(T), of position and momentum Shannon information entropies Sr and Sp is shown to be independent of the coupling strength scaling. The other commonly used uncertainty like products also follow similar behavior. The ramifications of this scaling property in the cases of hydrogenlike, harmonic oscillator, Morse, and Poeschl-Teller potentials are discussed with the example of S(T).
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Affiliation(s)
- K D Sen
- School of Chemistry, University of Hyderabad, Hyderabad 500 046, India.
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Sagar RP, Guevara NL. Mutual information and electron correlation in momentum space. J Chem Phys 2006; 124:134101. [PMID: 16613443 DOI: 10.1063/1.2180777] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Mutual information and information entropies in momentum space are proposed as measures of the nonlocal aspects of information. Singlet and triplet state members of the helium isoelectronic series are employed to examine Coulomb and Fermi correlations, and their manifestations, in both the position and momentum space mutual information measures. The triplet state measures exemplify that the magnitude of the spatial correlations relative to the momentum correlations depends on and may be controlled by the strength of the electronic correlation. The examination of one- and two-electron Shannon entropies in the triplet state series yields a crossover point, which is characterized by a localized momentum density. The mutual information density in momentum space illustrates that this localization is accompanied by strong correlation at small values of p.
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Affiliation(s)
- Robin P Sagar
- Departamento de Química, Universidad Autónoma Metropolitana Apartado Postal 55-534, Iztapalapa, 09340 México D.F., México
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