Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistical mechanical foundations of power-law distributions   The foundations of the Boltzmann-Gibbs (BG) distributions for describing
equilibrium statistical mechanics of systems are examined. Broadly, they fall
into: (i) probabilistic paaroaches based on the principle of equal a priori
probability (counting technique and method of steepest descents), law of large
numbers, or the state density considerations and (ii) a variational scheme --
maximum entropy principle (due to Gibbs and Jaynes) subject to certain
constraints. A minimum set of requirements on each of these methods are briefly
pointed out: in the first approach, the function space and the counting
algorithm while in the second, "additivity" property of the entropy with
respect to the composition of statistically independent systems. In the past
few decades, a large number of systems, which are not necessarily in
thermodynamic equilibrium (such as glasses, for example), have been found to
display power-law distributions, which are not describable by the
above-mentioned methods. In this paper, parallel to all the inquiries
underlying the BG program described above are given in a brief form. In
particular, in the probabilistic derivations, one employs a different function
space and one gives up "additivity" in the variational scheme with a different
form for the entropy. The requirement of stability makes the entropy choice to
be that proposed by Tsallis. From this a generalized thermodynamic description
of the system in a quasi-equilibrium state is derived. A brief account of a
unified consistent formalism associated with systems obeying power-law
distributions precursor to the exponential form associated with thermodynamic
equilibrium of systems is presented here.

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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
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The categories of this paper are: math
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: solv-int