Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistical mechanics for complex systems: On the structure of
  $q$-triplets   A plethora of natural, artificial and social complex systems exists which
violate the basic hypothesis (e.g., ergodicity) of Boltzmann-Gibbs (BG)
statistical mechanics. Many of such cases can be satisfactorily handled by
introducing nonadditive entropic functionals, such as $S_q\equiv
k\frac{1-\sum_{i=1}^W p_i^q}{q-1} \; \Bigl(q \in {\cal R}; \, \sum_{i=1}^W
p_i=1 \Bigr)$, with $S_1=S_{BG}\equiv -k\sum_{i=1}^W p_i \ln p_i$. Each class
of such systems can be characterized by a set of values $\{q\}$, directly
corresponding to its various physical/dynamical/geometrical properties. A most
important subset is usually referred to as the $q$-triplet, namely
$(q_{sensitivity}, q_{relaxation}, q_{stationary\,state})$, defined in the body
of this paper. In the BG limit we have
$q_{sensitivity}=q_{relaxation}=q_{stationary\,state}=1$. For a given class of
complex systems, the set $\{q\}$ contains only a few independent values of $q$,
all the others being functions of those few. An illustration of this structure
was given in 2005 [Tsallis, Gell-Mann and Sato, Proc. Natl. Acad. Sc. USA {\bf
102}, 15377; TGS]. This illustration enabled a satisfactory analysis of the
Voyager 1 data on the solar wind. But the general form of these structures
still is an open question. This is so, for instance, for the challenging
$q$-triplet associated with the edge of chaos of the logistic map. We introduce
here a transformation which sensibly generalizes the TGS one, and which might
constitute an important step towards the general solution.

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The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org