Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Open Journal of Chemistry

Equalization principles in open subsystems, origins of information descriptors and state-continuity relations

Nalewajski Roman F

Published Jan 6, 2021• 0 citations
Publisher

Abstract

The electronegativity-equalization at several hypothetical stages of chemical reactions is reexamined and phase-equalization in open substrates is explored. The equivalence of the energy and information reactivity criteria is stressed and local energy concept is shown to determine time-evolutions of wavefunction components. Independent sources of information content in electronic states are identifi ed and the need for resultant entropy-information measures in quantum mechanics, combining information contributions due to the classical (probability) and nonclassical (phase/current) distributions, is reemphasized. Limitations for a simultaneous removal of uncertainties in the position and velocity distributions imposed by the Heisenberg indeterminacy principle, are discussed, continuities of the wavefunction modulus and phase components are examined, the convectional character of the local source of resultant gradient information is stressed, and a latent (“horizontal”) probability currents in the stationary quantum states are discussed.

DOI
10.17352/ojc.000023

Related papers

Independent Sources of Information-Theoretic Descriptors of Electronic States

Roman F. Nalewajski

The need for resultant measures of the Information-Theoretic (IT) content of molecular electronic wavefunctions, combining the information contributions due to the probability and phase/current distributions, is reemphasized. Complementary measures of the state entropy (disorder) and information (order) contents are reexamined, the continuities of wavefunction components are summarized, and the probability acceleration concept is used to determine the current and information sources. The experimental elimination of the state uncertainties is discussed and limitations in this information-acquirement process imposed by the Heisenberg indeterminacy principle are commented upon.

Academic Journal of Chemistry•Dec 8, 2020•3 citations

Quantum information descriptors in position and momentum spaces

Roman F. Nalewajski

The resultant measures of the entropy/information content in complex electronic states are discussed in the canonical position and momentum representations of molecular quantum mechanics. The nonclassical (phase/current) supplements of the classical (probability) descriptors of the overall entropy/information content in electronic states are identified and the associated entropy deficiency (information distance) quantities are introduced. The Shannon (global, logarithmic) and Fisher (local, gradient) information descriptors in both spaces are summarized, and the momentum continuity equation is used to establish the associated probability source. General relations between global and local information densities are examined and the etropic principles determining molecular phase equilibria are investigated.

Journal of Mathematical Chemistry•May 20, 2015•7 citations

Information equilibria, subsystem entanglement, and dynamics of the overall entropic descriptors of molecular electronic structure

Roman F. Nalewajski

Overall descriptors of the information (determinicity) and entropy (uncertainty) content of complex molecular states are reexamined. These resultant concepts combine the classical (probability) contributions of Fisher and Shannon, and the relevant nonclassical supplements due to the state phase/current. The information-theoretic principles determining equilibria in molecules and their fragments are explored and the nonadditive part of the global entropy is advocated as a descriptor of the classical index of the quantum entanglement of molecular subsystems. Affinities associated with the probability and phase fluxes are identified and the criterion of vanishing overall information-source is shown to identify the system stationary electronic states. The production of resultant density of the gradient-information is expressed in terms of the conjugate affinities (forces, perturbations) and fluxes (currents, responses). The Schrödinger dynamics of probability and phase components of molecular electronic states is used to determine the temporal evolution of the overall gradient information and complex entropy. The global sources of the resultant information/entropy descriptors are shown to be of purely nonclassical origin, thus identically vanishing in real electronic states, e.g., the nondegenerate ground state of a molecule.

Journal of Molecular Modeling•Jul 19, 2018•17 citations

Information-Theoretic Descriptors of Molecular States and Electronic Communications between Reactants

Roman F. Nalewajski

The classical (modulus/probability) and nonclassical (phase/current) components of molecular states are reexamined and their information contributions are summarized. The state and information continuity relations are discussed and a nonclassical character of the resultant gradient information source is emphasized. The states of noninteracting and interacting subsystems in the model donor-acceptor reactive system are compared and configurations of the mutually-closed and -open equidensity orbitals are tackled. The density matrices for subsystems in reactive complexes are used to describe the entangled molecular fragments and electron communications in donor-acceptor systems which determine the entropic multiplicity and composition of chemical bonds between reactants.

Entropy•Jul 7, 2020•15 citations

Quantum Information Measures and Their Use in Chemistry

Roman F. Nalewajski

Background: The resultant measures of the information content in molecular electronic states are revisited. In these overall measures the current-related terms complement the probability functionals of classical Information Theory. The nonclassical Shannon entropy reflects the average magnitude of the state phase distribution, while the related current term in the complementary Fisher measure accounts for the average phase-gradient. Method: These generalized Fisher and Shannon descriptors of the information content in complex electronic states are applied to determine the phase-equilibria in molecules. The vertical and horizontal equilibria in molecules, which mark the extrema of the nonclassical and resultant entropy/information descriptors, respectively, are explored. The requirement, that the resultant measures have common solutions of the associated extreme entropy/information principles, calls for the negative sign of the nonclassical gradient measure. Conclusion: These extrema imply the phase-transformation of molecular electronic states. A separation of the density (modulus) and current (phase) factors in many-electron states is effected using the Harriman-Zumbach-Maschke construction of complex antisymmetric states yielding the specified electron density. A combined description of molecular systems, which accounts for the density and current degrees-of-freedom of electronic states is summarized and continuity equations for the state phase and resultant entropy are discussed. Keywords: Continuity equations, current-information, information continuity, molecular equilibria, phase-entropy/information, entropy.

Current Physical Chemistry•Sep 25, 2017•17 citations

On Temporal Evolution of Information-Theoretic Descriptors of Molecular Electronic Structure

Roman F. Nalewajski

The dynamics of probability (modulus) and phase (current) components of general electronic states is used to determine the temporal evolution of the overall descriptors of the information (determinicity) and entropy (indeterminicity) content of complex molecular states. These resultant information-theoretic concepts combine the classical (probability) contributions of Fisher and Shannon, and the corresponding nonclassical supplements due to the state phase/current. The total time derivatives of such overall measures of the gradient information and complex entropy are determined from Schrödinger’s equation using the chainrule transformations. These overall productions of the gradient information and complex entropy are shown to be of a purely nonclassical origin, thus identically vanishing in real electronic states, e.g., the nondegenerate ground state of a molecule.

Structural Chemistry & Crystallography Communication•Jan 1, 2018•0 citations
The electronegativity-equalization at several hypothetical stages of chemical reactions is reexamined and phase-equalization in open substrates is explored. The equivalence of the energy and information reactivity criteria is stressed and local energy concept is shown to determine time-evolutions of wavefunction components. Independent sources of information content in electronic states are identifi ed and the need for resultant entropy-information measures in quantum mechanics, combining information contributions due to the classical (probability) and nonclassical (phase/current) distributions, is reemphasized. Limitations for a simultaneous removal of uncertainties in the position and velocity distributions imposed by the Heisenberg indeterminacy principle, are discussed, continuities of the wavefunction modulus and phase components are examined, the convectional character of the local source of resultant gradient information is stressed, and a latent (“horizontal”) probability currents in the stationary quantum states are discussed.
The need for resultant measures of the Information-Theoretic (IT) content of molecular electronic wavefunctions, combining the information contributions due to the probability and phase/current distributions, is reemphasized. Complementary measures of the state entropy (disorder) and information (order) contents are reexamined, the continuities of wavefunction components are summarized, and the probability acceleration concept is used to determine the current and information sources. The experimental elimination of the state uncertainties is discussed and limitations in this information-acquirement process imposed by the Heisenberg indeterminacy principle are commented upon.
The resultant measures of the entropy/information content in complex electronic states are discussed in the canonical position and momentum representations of molecular quantum mechanics. The nonclassical (phase/current) supplements of the classical (probability) descriptors of the overall entropy/information content in electronic states are identified and the associated entropy deficiency (information distance) quantities are introduced. The Shannon (global, logarithmic) and Fisher (local, gradient) information descriptors in both spaces are summarized, and the momentum continuity equation is used to establish the associated probability source. General relations between global and local information densities are examined and the etropic principles determining molecular phase equilibria are investigated.
Overall descriptors of the information (determinicity) and entropy (uncertainty) content of complex molecular states are reexamined. These resultant concepts combine the classical (probability) contributions of Fisher and Shannon, and the relevant nonclassical supplements due to the state phase/current. The information-theoretic principles determining equilibria in molecules and their fragments are explored and the nonadditive part of the global entropy is advocated as a descriptor of the classical index of the quantum entanglement of molecular subsystems. Affinities associated with the probability and phase fluxes are identified and the criterion of vanishing overall information-source is shown to identify the system stationary electronic states. The production of resultant density of the gradient-information is expressed in terms of the conjugate affinities (forces, perturbations) and fluxes (currents, responses). The Schrödinger dynamics of probability and phase components of molecular electronic states is used to determine the temporal evolution of the overall gradient information and complex entropy. The global sources of the resultant information/entropy descriptors are shown to be of purely nonclassical origin, thus identically vanishing in real electronic states, e.g., the nondegenerate ground state of a molecule.
The classical (modulus/probability) and nonclassical (phase/current) components of molecular states are reexamined and their information contributions are summarized. The state and information continuity relations are discussed and a nonclassical character of the resultant gradient information source is emphasized. The states of noninteracting and interacting subsystems in the model donor-acceptor reactive system are compared and configurations of the mutually-closed and -open equidensity orbitals are tackled. The density matrices for subsystems in reactive complexes are used to describe the entangled molecular fragments and electron communications in donor-acceptor systems which determine the entropic multiplicity and composition of chemical bonds between reactants.
Background: The resultant measures of the information content in molecular electronic states are revisited. In these overall measures the current-related terms complement the probability functionals of classical Information Theory. The nonclassical Shannon entropy reflects the average magnitude of the state phase distribution, while the related current term in the complementary Fisher measure accounts for the average phase-gradient. Method: These generalized Fisher and Shannon descriptors of the information content in complex electronic states are applied to determine the phase-equilibria in molecules. The vertical and horizontal equilibria in molecules, which mark the extrema of the nonclassical and resultant entropy/information descriptors, respectively, are explored. The requirement, that the resultant measures have common solutions of the associated extreme entropy/information principles, calls for the negative sign of the nonclassical gradient measure. Conclusion: These extrema imply the phase-transformation of molecular electronic states. A separation of the density (modulus) and current (phase) factors in many-electron states is effected using the Harriman-Zumbach-Maschke construction of complex antisymmetric states yielding the specified electron density. A combined description of molecular systems, which accounts for the density and current degrees-of-freedom of electronic states is summarized and continuity equations for the state phase and resultant entropy are discussed. Keywords: Continuity equations, current-information, information continuity, molecular equilibria, phase-entropy/information, entropy.
The dynamics of probability (modulus) and phase (current) components of general electronic states is used to determine the temporal evolution of the overall descriptors of the information (determinicity) and entropy (indeterminicity) content of complex molecular states. These resultant information-theoretic concepts combine the classical (probability) contributions of Fisher and Shannon, and the corresponding nonclassical supplements due to the state phase/current. The total time derivatives of such overall measures of the gradient information and complex entropy are determined from Schrödinger’s equation using the chainrule transformations. These overall productions of the gradient information and complex entropy are shown to be of a purely nonclassical origin, thus identically vanishing in real electronic states, e.g., the nondegenerate ground state of a molecule.