Fisher information in density functional theory

Nagy, Á.

doi:10.1063/1.1615765

Cited by 111 publications

(73 citation statements)

References 32 publications

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“…For various applications of the Fisher information in physics and chemistry see e.g. (Chakrabarty, 2004;Hornyák & Nagy, 2007;Nagy, 2003;2006;2007;Nagy & Liu, 2008;Nagy & Sen, 2006;Romera & Nagy, 2008;Szabó et al, 2008). We start with normalization condition (5) for the probability density ρ in which we perform integration by parts…”

Section: Fisher Informationmentioning

confidence: 99%

Quantum Mechanics and Statistical Description of Results of Measurement

Skála¹,

Kapsa²

2012

Theoretical Concepts of Quantum Mechanics

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Section: Fisher Informationmentioning

confidence: 99%

Quantum Mechanics and Statistical Description of Results of Measurement

Skála¹,

Kapsa²

2012

Theoretical Concepts of Quantum Mechanics

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“…Let us finally remark that this quantity has been used (i) to describe, a factor apart, various macroscopic quantities, e.g. the kinetic [33,41,43,50] and Weissäcker [40,41,43], (ii) to derive the Schrödinger and Klein-Gordon equations of motion [24,39] as well as the Euler equation of the density functional theory [35] from the principle of minimum Fisher information, (iii) to predict the most distinctive non-linear phenomena (avoided crossings) encountered in atoms and molecules under strong external fields [26], and (iv) to measure the non-classicality of quantum systems [28,29], and (v) to obtain the foundations of thermodynamics in a microscopic way [25,37].…”

Section: The Fisher Informationmentioning

confidence: 99%

Fisher information of special functions and second-order differential equations

Yáñez

Sánchez-Moreno

Zarzo

et al. 2008

Journal of Mathematical Physics

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We investigate a basic question of information theory, namely the evaluation of the Fisher information and the relative Fisher information with respect to a nonnegative function, for the probability distributions obtained by squaring the special functions of mathematical physics which are solutions of second-order differential equations. Emphasis is made in the Nikiforov-Uvarov hypergeometric-type functions. We obtain explicit expressions for these information-theoretic properties via the expectation values of the coefficients of the differential equation. We illustrate our approach for various special functions of physico-mathematical interest.

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“…6,[9][10][11][12][13] In the next sections, we report the main aspects of the procedure in order to introduce the reader to the new conceptual and numerical aspects and we then show results for the nearly uniform electron gas. Appendix A reports relevant technical aspects of the MC calculations.…”

Section: Introductionmentioning

confidence: 99%

“…The results showed that the kinetic-energy functional could be written as the sum of two terms from information theory. 4 One term resembles the Fisher information 5,6 ͑analytical result͒, which is a measure of localization. The other term resembles the Shannon entropy 7 ͑numerical result͒, which is a measure of delocalization.…”

Section: Introductionmentioning

confidence: 99%

Interacting electrons, spin statistics, and information theory

Ghiringhelli

Hamilton

Site

2010

The Journal of Chemical Physics

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We consider a nearly ͑or quasi͒ uniform gas of interacting electrons for which spin statistics play a crucial role. A previously developed procedure, based on the extension of the Levy-Lieb constrained search principle and Monte Carlo sampling of electron configurations in space, allows us to approximate the form of the kinetic-energy functional. For a spinless electron gas, this procedure led to a correlation term, which had the form of the Shannon entropy, but the resulting kinetic-energy functional does not satisfy the Lieb-Thirring inequality, which is rigorous and one of the most general relations regarding the kinetic energy. In this paper, we show that when the fermionic character of the electrons is included via a statistical spin approach, our procedure leads to correlation terms, which also have the form of the Shannon entropy and the resulting kinetic-energy functional does satisfy the Lieb-Thirring inequality. In this way we further strengthen the connection between Shannon entropy and electron correlation and, more generally, between information theory and quantum mechanics.

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Fisher information in density functional theory

Abstract: The Euler equation of the density functional theory is derived from the principle of minimum Fisher information. Both time-independent and time-dependent cases are analyzed. It is shown that Fisher information is a measure of the quality of the approximate density.

Cited by 111 publications

References 32 publications

Quantum Mechanics and Statistical Description of Results of Measurement

Quantum Mechanics and Statistical Description of Results of Measurement

Fisher information of special functions and second-order differential equations

Interacting electrons, spin statistics, and information theory

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