Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Ehrenfest's Equations and phase transition in Black Holes   We generalize Ehrenfest's equations to systems having two work terms, i.e.
systems with three degrees of freedom. For black holes with two work terms we
obtain nine equations instead of two to be satisfied at the critical point of a
second order phase transition. We finally generalize this method to a system
with an arbitrary number of degrees of freedom and found there is
$\frac{N(N+1)^{2}}{2}$ equations to be satisfied at the point of a second order
phase transition where $N$ is number of work terms in the first law of
thermodynamics.

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The categories of this paper are: physics
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
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The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: math