Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Possible thermodynamic structure underlying the laws of Zipf and Benford   We show that the laws of Zipf and Benford, obeyed by scores of numerical data
generated by many and diverse kinds of natural phenomena and human activity are
related to the focal expression of a generalized thermodynamic structure. This
structure is obtained from a deformed type of statistical mechanics that arises
when configurational phase space is incompletely visited in a severe way.
Specifically, the restriction is that the accessible fraction of this space has
fractal properties. The focal expression is an (incomplete) Legendre transform
between two entropy (or Massieu) potentials that when particularized to first
digits leads to a previously existing generalization of Benford's law. The
inverse functional of this expression leads to Zipf's law; but it naturally
includes the bends or tails observed in real data for small and large rank.
Remarkably, we find that the entire problem is analogous to the transition to
chaos via intermittency exhibited by low-dimensional nonlinear maps. Our
results also explain the generic form of the degree distribution of scale-free
networks.

14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
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The categories of this paper are: eess
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom