Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entanglement density and gravitational thermodynamics   In an attempt to find a quasi-local measure of quantum entanglement, we
introduce the concept of entanglement density in relativistic quantum theories.
This density is defined in terms of infinitesimal variations of the region
whose entanglement we monitor, and in certain cases can be mapped to the
variations of the generating points of the associated domain of dependence. We
argue that strong sub-additivity constrains the entanglement density to be
positive semi-definite. Examining this density in the holographic context, we
map its positivity to a statement of integrated null energy condition in the
gravity dual. We further speculate that this may be mapped to a statement
analogous to the second law of black hole thermodynamics, for the extremal
surface.

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The categories of this paper are: math
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg