Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Equilibrium states and their entropy densities in gauge-invariant
  C*-systems
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
19
The categories of this paper are: eess
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol