Fisher information and density functional theory

Nagy, Á.

doi:10.1002/qua.26679

Cited by 13 publications

(15 citation statements)

References 127 publications

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“…Fisher focused on the quantity of information that is acquired (and, as well, the amount of information lost) in the process of a measurement. This approach is broadly used in virtually every scientific discipline including biology (7), psychology (6), physics (8) and chemistry (9) in a measurement Unlike Shannnon information, because Fisher Information is derived from physical measurement, it assumes the units of the associated physical processes (20)(21)(22)(23)(24).…”

Section: Introductionmentioning

confidence: 99%

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Converting genetic information to non-equilibrium cellular thermodynamics in enzyme-catalyzed reactions

Gatenby

2023

Preprint

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Living systems use genomic information to maintain a stable highly ordered state far from thermodynamic equilibrium but the specific mechanisms and general principles governing the interface of genetics and thermodynamics has not been extensively investigated. Genetic information is quantified in unitless bits termed Shannon entropy, which does not directly relate to thermodynamic entropy or energy. Thus, it is unclear how the Shannon entropy of genetic information is converted into thermodynamic work necessary to maintain the non-equilibrium state of living systems. Here we investigate the interface of genetic information and cellular thermodynamics in enzymatic acceleration of a chemical reaction. The rate of any intracellular chemical reaction is determined by probability functions at macroscopic, Boltzmann distribution of the reactant kinetic energies governed by temperature, or microscopic, overlap of reactant quantum wave functions, scales, described, respectively, by the Arrhenius and Knudsen equations. That is, the reaction rate, in the absence of a catalyst, is governed by temperature which determines the kinetic energy of the interacting molecules. Genetic information can act upon a when the encoded string of amino acids folds into a 3 dimensional structure that permits a lock/key spatial matching with the reactants. By optimally superposing the reactants wave functions, the information in the enzyme increases the reaction rate by up to 15 orders of magnitude under isothermal conditions. In turn, the accelerated reaction rate alters the intracellular thermodynamics environment as the products are at lower Gibbs free energy which permits thermodynamic work. Mathematically and biologically, the critical event that allows genetic information to produce thermodynamic work is the folding of the amino acid string specified by the gene into a 3dimensional shape determined by its lowest energy state. Biologically, this allows the amino acid string to bind substrate and place them in an optimal spatial orientation. These key-lock are mathematically characterized by Kullback Leibler Divergence and the interactions with the reaction channel now represent Fisher Information, the second derivative of the Kullback Leibler divergence, which can take on the units of the process to which it is applied. Interestingly, Shannon is typically derived by coarse graining Shannon information. Thus, living system, by acting at a quantum level, fine grain Shannon information.

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Section: Introductionmentioning

confidence: 99%

“…Critical to our analysis here, Shannon and Fisher Information are related (8) as the former emerges from course graining (transitioning from a continuous to a discrete function dx →∆x) of the latter. Thus, because genetic information is encoded as discrete quantities (i.e.…”

Section: Introductionmentioning

confidence: 99%

Converting genetic information to non-equilibrium cellular thermodynamics in enzyme-catalyzed reactions

Gatenby

2023

Preprint

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“…The Shannon entropy and complexity of triaxial nuclei was investigated very recently via the Bohr Hamiltonian [28]. More literature on quantum information can be found in the following works [29][30][31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Quantum information of the modified Mobius squared plus Eckart potential

Njoku

Onyeocha

Onyenegecha

et al. 2022

Int J of Quantum Chemistry

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The quantum information measures and complexity of the modified Mobius squared plus Eckart (MMSE) potential are presented in this paper. First, the energy eigenvalues and wave function of the system are obtained from the approximate solutions of the Schrödinger equation via the parametric Nikiforov-Uvarov (pNU) method.Using the wave function, the Shannon entropy, Onicescu information energy and Fisher information of the system are examined for two low-lying states along with the modified Lopez-Ruiz-Mancini-Calbet (LMC) complexity and Heisenberg uncertainty relation. The results of the work point to the fact that the radial (momentum) probability density peak shifts to lower (higher) values with increase in the screening parameter. Furthermore, the Bialynicki-Birula and Mycielski (BBM) inequality, the lower bound of the modified LMC complexity, the Fisher information sum inequality and the Stam-Cramer-Rao inequality are verified for the system. Also, the Heisenberg uncertainty principle is verified for the MMSE potential and the existence of squeezed states is observed for both position and momentum states.

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“…Consider distribution functions depending on a parameter θ and the fidelity with functions fðθÞ and fðθ þ δθÞ. Then we arrive at the fidelity susceptibility χ [27,33] χ ¼ 1 4…”

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confidence: 99%

“…Consider now the relative Rényi entropy for the distribution functions fðθÞ and fðθ þ δθÞ. Expanding fðθ þ δθÞ around fðθÞ we are led to [27,34,35] R q fðθÞ,fðθþδθÞ ≈ 2qχðδθÞ 2 : ð9Þ…”

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confidence: 99%

Phase‐space relative Rényi entropy in density functional theory

Nagy

2023

Int J of Quantum Chemistry

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The phase‐space relative Rényi entropy is introduced using the information theoretical and thermodynamic view of density functional theory. In the special case of constant inverse temperature the phase‐space relative Rényi entropy is a sum of the position‐space relative Rényi entropy and a term arising from the momentum space. This quantity can be considered as a measure of similarity. It includes more information than the position‐space measures, since it also incorporates momentum‐space knowledge.

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Fisher information and density functional theory

Cited by 13 publications

References 127 publications

Converting genetic information to non-equilibrium cellular thermodynamics in enzyme-catalyzed reactions

Converting genetic information to non-equilibrium cellular thermodynamics in enzyme-catalyzed reactions

Quantum information of the modified Mobius squared plus Eckart potential

Phase‐space relative Rényi entropy in density functional theory

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