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- Title
Complex entropy and resultant information measures.
- Authors
Nalewajski, Roman
- Abstract
Classical and nonclassical contributions to Author's resultant Shannon- and Fisher-type measures of the information content in general electronic state $$\varphi ( {\varvec{r}} ) =R( {\varvec{r}}) \hbox { exp}[\hbox {i}\phi ( {\varvec{r}} )]$$ , due to the state probability density $$p( {\varvec{r}} ) =R( {\varvec{r}} )^{2}$$ and its phase $$\phi ( {\varvec{r}} )$$ or current $${\varvec{j}}( {\varvec{r}} )=\left( \hbar /m \right) p( {\varvec{r}} )\nabla \phi \left( {\varvec{r}} \right) $$ distributions, respectively, are reexamined. The components of the overall entropy, are shown to determine the real and imaginary parts of the state complex Shannon entropy, a natural quantum-amplitude generalization of the classical Shannon entropy. Its contributions are related to the associated terms in the state resultant Fisher information, and the gradient entropy:
- Subjects
NONCLASSICAL mathematical logic; ENTROPY (Information theory); GENERALIZATION; FISHER information; PROBABILITY density function
- Publication
Journal of Mathematical Chemistry, 2016, Vol 54, Issue 9, p1777
- ISSN
0259-9791
- Publication type
Article
- DOI
10.1007/s10910-016-0651-6