Phase/current information descriptors and equilibrium states in molecules

Quantum‐generalized entropic descriptors of the complex electronic states and their information distances are reexamined and applied to the phase‐equilibria in molecules. The relation between densities of the ordinary Fisher and Shannon measures of information content is used in determining their supplements due to phases/currents. These nonclassical terms complement the familiar classical (probability) functionals of information theory in the resultant information descriptors. The nonclassical Shannon entropy measures the average magnitude of the system phase distribution, while the current term in the related Fisher measure accounts for the gradient content of the state phase. The density constrained (vertical) and unconstrained (horizontal) equilibria in molecules are distinguished. The consistency requirement that the extreme entropic principles in terms of both these resultant measures have common solutions calls for the modified, negative sign of the nonclassical Fisher indeterminicity term. The equilibrium criteria are shown to give rise to the unitary phase‐transformation of molecular states in a “thermodynamic” representation of quantum‐mechanical description. Possible applications of this generalized description are discussed and thermodynamical analogies are commented upon. A separation of the density (modulus) and current (phase) factors of general many‐electron states is effected using the Harriman–Zumbach–Maschke construction of antisymmetric states yielding the specified electron density. A phenomenological description of molecular subsystems is outlined, which accounts for both the density and phase degrees‐of‐freedom of electronic states, and the current promotion of molecular fragments is explored. © 2014 Wiley Periodicals, Inc. Information‐theoretic description of electronic states requires the classical (probability) descriptors and their nonclassical (current) complements. The unconstrained extremum of the resultant entropy/information content determines the phase‐transformed equilibrium state, which differs from the stationary (zero‐current) state of quantum mechanics. The nonclassical supplements to the familiar classical measures, global (Shannon), and local (Fisher), are designed and current promotion of molecular fragments is explored. This fully quantum information–theoretic approach generates thermodynamic perspective on time evolution of equilibrium states.