Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Formulation of R\'enyi Entropy on $C^*$-Algebras   The entropy of probability distribution defined by Shannon has several
extensions. R\'enyi entropy is one of the general extensions of Shannon entropy
and is widely used in engineering, physics, and so on. On the other hand, the
quantum analogue of Shannon entropy is von Neumann entropy. Furthermore, the
formulation of this entropy was extended to on $C^*$-algebras by Ohya
($\mathcal{S}$-mixing entropy). In this paper, we formulate Renyi entropy on
$C^*$-algebras based on $\mathcal{S}$-mixing entropy and prove several
inequalities for the uncertainties of states in various reference systems.

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The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th