Differential Entropy on Statistical Spaces

Details Differential Entropy on Statistical Spaces Differential Entropy on Statistical Spaces

2005-05-16

arxiv.org/abs/cond-mat/0505397v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, to appear in the proceedings of the joint meeting of the 2nd International Conference on Cybernetics and Information

Scientific paper

We show that the previously introduced concept of distance on statistical spaces leads to a straightforward definition of differential entropy on these statistical spaces. These spaces are characterized by the fact that their points can only be localized within a certain volume and exhibit thus a feature of fuzziness. This implies that Riemann integrability of relevant integrals is no longer secured. Some discussion on the specialization of this formalism to quantum states concludes the paper.

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