Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A coarse-grained generalized second law for holographic conformal field
  theories   We consider the universal sector of a $d$-dimensional large-$N$
strongly-interacting holographic CFT on a black hole spacetime background $B$.
When our CFT$_d$ is coupled to dynamical Einstein-Hilbert gravity with Newton
constant $G_{d}$, the combined system can be shown to satisfy a version of the
thermodynamic Generalized Second Law (GSL) at leading order in $G_{d}$. The
quantity $S_{CFT} + \frac{A(H_{B, \text{perturbed}})}{4G_{d}}$ is
non-decreasing, where $A(H_{B, \text{perturbed}})$ is the (time-dependent) area
of the new event horizon in the coupled theory. Our $S_{CFT}$ is the notion of
(coarse-grained) CFT entropy outside the black hole given by causal holographic
information -- a quantity in turn defined in the AdS$_{d+1}$ dual by the
renormalized area $A_{ren}(H_{\rm bulk})$ of a corresponding bulk causal
horizon. A corollary is that the fine-grained GSL must hold for finite
processes taken as a whole, though local decreases of the fine-grained
generalized entropy are not obviously forbidden. Another corollary, given by
setting $G_{d} = 0$, states that no finite process taken as a whole can
increase the renormalized free energy $F = E_{out} - T S_{CFT} - \Omega J -
\Phi Q$, with $T, \Omega, \Phi$ constants set by ${H}_B$. This latter corollary
constitutes a 2nd law for appropriate non-compact AdS event horizons.

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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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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: math
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The categories of this paper are: chem-ph
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The categories of this paper are: cs