Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigorous results in non-extensive thermodynamics   This paper studies quantum systems with a finite number of degrees of freedom
in the context of non-extensive thermodynamics. A trial density matrix,
obtained by heuristic methods, is proved to be the equilibrium density matrix.
If the entropic parameter q is larger than 1 then existence of the trial
equilibrium density matrix requires that q is less than some critical value q_c
which depends on the rate by which the eigenvalues of the hamiltonian diverge.
Existence of a unique equilibrium density matrix is proved if in addition q<2
holds. For q between 0 and 1, such that 2<q+q_c, the free energy has at least
one minimum in the set of trial density matrices. If a unique equilibrium
density matrix exists then it is necessarily one of the trial density matrices.
Note that this is a finite rank operator, which means that in equilibrium high
energy levels have zero probability of occupancy.

10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat