Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Relationship between Tsallis Statistics, the Fourier Transform, and
  Nonlinear Coupling   Tsallis statistics (or q-statistics) in nonextensive statistical mechanics is
a one-parameter description of correlated states. In this paper we use a
translated entropic index: $1 - q \to q$ . The essence of this translation is
to improve the mathematical symmetry of the q-algebra and make q directly
proportional to the nonlinear coupling. A conjugate transformation is defined
$\hat q \equiv \frac{{- 2q}}{{2 + q}}$ which provides a dual mapping between
the heavy-tail q-Gaussian distributions, whose translated q parameter is
between $ - 2 < q < 0$, and the compact-support q-Gaussians, between $0 < q <
\infty $ . This conjugate transformation is used to extend the definition of
the q-Fourier transform to the domain of compact support. A conjugate q-Fourier
transform is proposed which transforms a q-Gaussian into a conjugate $\hat q$
-Gaussian, which has the same exponential decay as the Fourier transform of a
power-law function. The nonlinear statistical coupling is defined such that the
conjugate pair of q-Gaussians have equal strength but either couple
(compact-support) or decouple (heavy-tail) the statistical states. Many of the
nonextensive entropy applications can be shown to have physical parameters
proportional to the nonlinear statistical coupling.

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The categories of this paper are: chem-ph
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics