Complex entropy and resultant information measures

Abstract

Classical and nonclassical contributions to Author’s resultant Shannon- and Fisher-type measures of the information content in general electronic state φ(r)=R(r)exp[iϕ(r)], due to the state probability density p(r) = R(r) 2 and its phase ϕ(r) or current j(r) = (ħ/ m) p(r) ∇ ϕ(r) distributions, respectively, are reexamined. The components of the overall entropy, (Formula presented.) are shown to determine the real and imaginary parts of the state complex Shannon entropy, (Formula presented.) a natural quantum-amplitude generalization of the classical Shannon entropy. Its contributions are related to the associated terms in the state resultant Fisher information, (Formula presented.) and the gradient entropy: (Formula presented.).