Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Properties of a Generalized Divergence Related to Tsallis Relative
  Entropy   In this paper, we investigate the partition inequality, joint convexity, and
Pinsker's inequality, for a divergence that generalizes the Tsallis Relative
Entropy and Kullback-Leibler divergence. The generalized divergence is defined
in terms of a deformed exponential function, which replaces the Tsallis
$q$-exponential. We also constructed a family of probability distributions
related to the generalized divergence. We found necessary and sufficient
conditions for the partition inequality to be satisfied. A sufficient condition
for the joint convexity was established. We proved that the generalized
divergence satisfies the partition inequality, and is jointly convex, if, and
only if, it coincides with the Tsallis relative entropy. As an application of
partition inequality, a criterion for the Pinsker's inequality was found.

34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph