Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fundamental thermodynamical equation of a self-gravitating system   The features of the fundamental thermodynamical relation (expressing entropy
as function of state variables) that arise from the self-gravitating character
of a system are analyzed. The models studied include not only a spherically
symmetric hot matter shell with constant particle number but also a black hole
characterized by a general thermal equation of state. These examples illustrate
the formal structure of thermodynamics developed by Callen as applied to a
gravitational configuration as well as the phenomenological manner in which
Einstein equations largely determine the thermodynamical equations of state. We
consider in detail the thermodynamics and quasi-static collapse of a
self-gravitating shell. This includes a discussion of intrinsic stability for a
one-parameter family of thermal equations of state and the interpretation of
the Bekenstein bound. The entropy growth associated with a collapsing sequence
of equilibrium states of a shell is computed under different boundary
conditions in the quasi-static approximation and compared with black hole
entropy. Although explicit expressions involve empirical coefficients, these
are constrained by physical conditions of thermodynamical origin. The absence
of a Gibbs-Duhem relation and the associated scaling laws for self-gravitating
matter systems are presented.

13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat