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The First Law of Complexity

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arxiv 1903.04511 v2 pith:5CCKNSVG submitted 2019-03-11 hep-th quant-ph

Alice Bernamonti , Federico Galli , Juan Hernandez , Robert C. Myers , Shan-Ming Ruan , Joan Simón This is my paper · ORCID
classification hep-thquant-ph
keywords complexityvariationactionboundaryfieldfirstscalarappears
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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".

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  1. CFT Complexity and Penalty Factors

    hep-th 2025-07 conditional novelty 6.0 of 10

    A submersion-based method turns weighted generator costs into state-complexity metrics for CFTs, giving analytic formulas in simple limits and constraints on which weight choices are viable.

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