Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thermodynamics with long-range interactions: from Ising models to
  black-holes   New methods are presented which enables one to analyze the thermodynamics of
systems with long-range interactions. Generically, such systems have entropies
which are non-extensive, (do not scale with the size of the system). We show
how to calculate the degree of non-extensivity for such a system. We find that
a system interacting with a heat reservoir is in a probability distribution of
canonical ensembles. The system still possesses a parameter akin to a global
temperature, which is constant throughout the substance. There is also a useful
quantity which acts like a {\it local temperatures} and it varies throughout
the substance. These quantities are closely related to counterparts found in
general relativity. A lattice model with long-range spin-spin coupling is
studied. This is compared with systems such as those encountered in general
relativity, and gravitating systems with Newtonian-type interactions. A
long-range lattice model is presented which can be seen as a black-hole analog.
One finds that the analog's temperature and entropy have many properties which
are found in black-holes. Finally, the entropy scaling behavior of a
gravitating perfect fluid of constant density is calculated. For weak
interactions, the entropy scales like the volume of the system. As the
interactions become stronger, the entropy becomes higher near the surface of
the system, and becomes more area-scaling.

30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
2
The categories of this paper are: math
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th