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

Abstract

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.