Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial Entropy for Distinguishable Entities in Indistinguishable
  States   The combinatorial basis of entropy by Boltzmann can be written $H= {N}^{-1}
\ln \mathbb{W}$, where $H$ is the dimensionless entropy of a system, per unit
entity, $N$ is the number of entities and $\mathbb{W}$ is the number of ways in
which a given realization of the system can occur, known as its statistical
weight. Maximizing the entropy (``MaxEnt'') of a system, subject to its
constraints, is then equivalent to choosing its most probable (``MaxProb'')
realization. For a system of distinguishable entities and states, $\mathbb{W}$
is given by the multinomial weight, and $H$ asymptotically approaches the
Shannon entropy. In general, however, $\mathbb{W}$ need not be multinomial,
leading to different entropy measures. This work examines the allocation of
distinguishable entities to non-degenerate or equally degenerate,
indistinguishable states. The non-degenerate form converges to the Shannon
entropy in some circumstances, whilst the degenerate case gives a new entropy
measure, a function of a multinomial coefficient, coding parameters, and
Stirling numbers of the second kind.

3
The categories of this paper are: physics
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
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The categories of this paper are: cs
11
The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
16
The categories of this paper are: stat