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arXiv · 1612.07769

A First Law of Entanglement Rates from Holography

Andy O'Bannon·Jonas Probst·Ronnie Rodgers·Christoph F. Uhlemann
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Abstract

For a perturbation of the state of a Conformal Field Theory (CFT), the response of the entanglement entropy is governed by the so-called "first law" of entanglement entropy, in which the change in entanglement entropy is proportional to the change in energy. Whether such a first law holds for other types of perturbations, such as a change to the CFT Lagrangian, remains an open question. We use holography to study the evolution in time $t$ of entanglement entropy for a CFT driven by a $t$-linear source for a conserved $U(1)$ current or marginal scalar operator. We find that although the usual first law of entanglement entropy may be violated, a first law for the rates of change of entanglement entropy and energy still holds. More generally, we prove that this first law for rates holds in holography for any asymptotically $(d+1)$-dimensional Anti-de Sitter metric perturbation whose $t$ dependence first appears at order $z^d$ in the Fefferman-Graham expansion about the boundary at $z=0$.

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Andy O'Bannon, Jonas Probst, Ronnie Rodgers, Christoph F. Uhlemann. 2016-12-22. A First Law of Entanglement Rates from Holography. https://doi.org/10.1103/physrevd.96.066028

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