Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Holographic Thermodynamics Requires a Chemical Potential for Color   The thermodynamic Euler equation for high-energy states of large-$N$ gauge
theories is derived from the dependence of the extensive quantities on the
number of colors $N$. This Euler equation relates the energy of the state to
the temperature, entropy, number of degrees of freedom and its chemical
potential, but not to the volume or pressure. In the context of the
gauge/gravity duality we show that the Euler equation is dual to the
generalized Smarr formula for black holes in the presence of a negative
cosmological constant. We also match the fundamental variational equation of
thermodynamics to the first law of black hole mechanics, when extended to
include variations of the cosmological constant and Newton's constant.

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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: bayes-an