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- W2246957787 abstract "Generalizing the first law of thermodynamics, the increase in entropy density $ensuremath{delta}S(x)$ of a conformal field theory (CFT) is proportional to the increase in energy density, $ensuremath{delta}E(x)$, of a subsystem divided by a spatially dependent entanglement temperature, ${T}_{E}(x)$, a fixed parameter determined by the geometry of the subsystem, crossing over to thermodynamic temperature at high temperatures. In this paper we derive a generalization of the thermodynamic Clausius relation, showing that deformations of the CFT by marginal operators are associated with spatial temperature variations, $ensuremath{delta}{T}_{E}(x)$, and spatial energy correlations play the role of specific heat. Using AdS/CFT duality we develop a relationship between a perturbation in the local entanglement temperature of the CFT and the perturbation of the bulk AdS metric. In two dimensions, we demonstrate a method through which direct diagonalizations of the boundary quantum theory may be used to construct geometric perturbations of ${mathrm{AdS}}_{3}$." @default.
- W2246957787 created "2016-06-24" @default.
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- W2246957787 date "2016-06-07" @default.
- W2246957787 modified "2023-09-26" @default.
- W2246957787 title "Entanglement temperature and perturbedAdS3geometry" @default.
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- W2246957787 doi "https://doi.org/10.1103/physrevd.93.126002" @default.
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