Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The First Law of Complexity   We investigate the variation of holographic complexity for two nearby target
states. Based on Nielsen's geometric approach, we find the variation only
depends on the end point of the optimal trajectory, a result which we designate
the first law of complexity. As an example, we examine the complexity=action
conjecture when the AdS vacuum is perturbed by a scalar field excitation, which
corresponds to a coherent state. Remarkably, the gravitational contributions
completely cancel and the final variation reduces to a boundary term coming
entirely from the scalar field action. Hence the null boundary of
Wheeler-DeWitt patch appears to act like the "end of the quantum circuit".

35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
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The categories of this paper are: eess
14
The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom