1. Complex entropy and resultant information measures.
- Author
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Nalewajski, Roman
- Subjects
- *
NONCLASSICAL mathematical logic , *ENTROPY (Information theory) , *GENERALIZATION , *FISHER information , *PROBABILITY density function - 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: [ABSTRACT FROM AUTHOR]
- Published
- 2016
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