Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On local quantum Gibbs states   We address in this work the problem of minimizing quantum entropies under
local constraints. We suppose macroscopic quantities such as the particle
density, current, and kinetic energy are fixed at each point of $\Rm^d$, and
look for a density operator over $L^2(\Rm^d)$ minimizing an entropy functional.
Such minimizers are referred to as a local Gibbs states. This setting is in
constrast with the classical problem of prescribing global constraints, where
the total number of particles, total current, and total energy in the system
are fixed. The question arises for instance in the derivation of fluid models
from quantum dynamics. We prove, under fairly general conditions, that the
entropy admits a unique constrained minimizer. Due to a lack of compactness,
the main difficulty in the proof is to show that limits of minimizing sequences
satisfy the local energy constraint. We tackle this issue by introducing a
simpler auxiliary minimization problem and by using a monotonicity argument
involving the entropy.

9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom