Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Is Sharma-Mittal entropy really a step beyond Tsallis and Renyi
  entropies?   We studied the Sharma-Mittal relative entropy and showed that its physical
meaning is the free energy difference between the off-equilibrium and
equilibrium distributions. Unfortunately, Sharma-Mittal relative entropy may
acquire this physical interpretation only in the limiting case when both
parameters approach to 1 in which case it approaches Kullback-Leibler entropy.
We also note that this is exactly how R\'{e}nyi relative entropy behaves in the
thermostatistical framework thereby suggesting that Sharma-Mittal entropy must
be thought to be a step beyond not both Tsallis and R\'{e}nyi entropies but
rather only as a generalization of R\'{e}nyi entropy from a thermostatistical
point of view. Lastly, we note that neither of them conforms to the
Shore-Johnson theorem which is satisfied by Kullback-Leibler entropy and one of
the Tsallis relative entropies.

9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin