Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of complex systems by their sample-space scaling
  exponents   The nature of statistics, statistical mechanics and consequently the
thermodynamics of stochastic systems is largely determined by how the number of
states $W(N)$ depends on the size $N$ of the system. Here we propose a scaling
expansion of the phasespace volume $W(N)$ of a stochastic system. The
corresponding expansion coefficients (exponents) define the universality class
the system belongs to. Systems within the same universality class share the
same statistics and thermodynamics. For sub-exponentially growing systems such
expansions have been shown to exist. By using the scaling expansion this
classification can be extended to all stochastic systems, including correlated,
constraint and super-exponential systems. The extensive entropy of these
systems can be easily expressed in terms of thee scaling exponents. Systems
with super-exponential phasespace growth contain important systems, such as
magnetic coins that combine combinatorial and structural statistics. We discuss
other applications in the statistics of networks, aging, and cascading random
walks.

7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org