Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entropy, Extremality, Euclidean Variations, and the Equations of Motion   We study the Euclidean gravitational path integral computing the Renyi
entropy and analyze its behavior under small variations. We argue that, in
Einstein gravity, the extremality condition can be understood from the
variational principle at the level of the action, without having to solve
explicitly the equations of motion. This set-up is then generalized to
arbitrary theories of gravity, where we show that the respective entanglement
entropy functional needs to be extremized. We also extend this result to all
orders in Newton's constant $G_N$, providing a derivation of quantum
extremality. Understanding quantum extremality for mixtures of states provides
a generalization of the dual of the boundary modular Hamiltonian which is given
by the bulk modular Hamiltonian plus the area operator, evaluated on the
so-called modular extremal surface. This gives a bulk prescription for
computing the relative entropies to all orders in $G_N$. We also comment on how
these ideas can be used to derive an integrated version of the equations of
motion, linearized around arbitrary states.

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The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat