On probability flow descriptors in position and momentum spaces

The current density concepts of the position and momentum probability distributions are examined and the associated continuity equations are explored. The modified flow measure in the momentum-space is introduced in terms of which the nonclassical (current-related) functionals of the entropy/information content in quantum states assume forms isomorphic with the corresponding position-space expressions, when expressed in terms of the state modulus (density) and phase (current) degrees-of-freedom. These concepts are illustrated for the stationary states as well as the plane waves and wave packets of the free particle

Quantum information approach to electronic equilibria : molecular fragments and non-equilibrium thermodynamic description

The quantum-generalized Information Theory is applied to explore mole- cular equilibrium states by using the resultant information content of electronic states, determind by the classical (probability based) measures and their non -classical (phase/current related) complements, in the extremum entropy/information princi- ples.The“ vertical ”(probability-constrained)entropicrulesareinvestigatedwithinthe familiar Levy and Harriman–Zumbach–Maschke constructions of Density Functional Theory. A close parallelism between the vertical maximum-entropy and minimum- energy principles in quantum mechanics and their thermodynamic analogs is empha- sized and a relation between the probability and phase distributions in the “ horizontal ” (probability-unconstrained) phase -equilibria is examined. These solutions are shown to involve the spatial phase contribution related to the system electron density.The complete specification of the equilibrium states of molecular/promolecular fragments, including the subsystem density and the equilibrium phase of the system as a whole, is advocatedandillustratedforbondedhydrogensinH 2 .Elementsofthe non -equilibrium thermodynamic description of molecular systems are formulated. They recognize the independent probability and phase state parameters, the associated currents, and their contributions to the quantum entropy density and its current. The phase and entropy continuity equations are explored and the local sources of these quantities are identi- fied

Quantum information descriptors in position and momentum spaces

The resultant measures of the entropy/information content in complex elec- tronic 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 dis- tance) 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

Communications in molecules : local and multi-configuration channels and their entropic descriptors of bond multiplicity and composition

The Orbital Communication Theory of the chemical bond, in which mole- cules are treated as information systems transmitting “signals” of electron allocations to Atomic Orbitals, is extended to cover the local resolution level of electron dis- tributions and the Configuration-Interaction (CI, multi -determinantal) description of molecular states. These communication systems generate the information-theoretic measures of both the absolute and relative multiplicities of chemical bonds, as well as the bond covalent (communication-noise) and ionic (information-flow) components. The orbital/local communications via the CI ensembles of the occupied molecular orbitals in such generalized molecular states are investigated. Illustrative two -orbital model and its prototype Valence-Bond structures are examined in a more detail

Entropic representation in the theory of molecular electronic structure

The entropic perspective on the molecular electronic structure is investigated. Information-theoretic description of electron probabilities is extended to cover thecomplexamplitudes(wavefunctions)ofquantummechanics.This analysis emphasizes the entropic concepts due to the phase part of electronic states, which generates the probability currentdensity, thus allowing one to distinguish the information content of states generating the same electron density and differing in their current densities. The classical information measures of Fisher and Shannon, due to the probability/density distributions themselves, are supplemented by the nonclassical terms generated by the wave-function phase or the associated probability current. A complementary character of the Fisher and Shannon information measures is explored and the relationship between these classical information densities is derived. It is postulated to characterize also their nonclassical (phase/current-dependent) contributions. The continuity equations of the generalized information densities are examined and the associated nonclassical information sources are identified. The variational rules involving the quantum-generalized Shannon entropy, which generate the stationary and time-dependent Schrödinger equations from the relevant maximum entropy principles, are discussed and their implications for the system “thermodynamic” equilibrium states are examined. It is demonstrated that the lowest, stationary “thermodynamic” state differs from the true ground state of the system, by exhibiting the space-dependent phase, linked to the modulus part of the wave function, and hence also a nonvanishing probability current