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Relative Entropy in de Sitter is a Noether Charge
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We compute the relative entropy between the vacuum and a coherent state for a massive scalar field in de Sitter spacetime, using Tomita-Takesaki modular theory and the Araki-Uhlmann formula for the relative entropy. Embedding de Sitter spacetime as a hyperboloid in the ambient Minkowski space, we can restrict the Minkowski wedge and the corresponding modular operator to de Sitter, and we verify that this construction gives the correct modular flow. We check that the relative entropy is positive and jointly convex, relate it to the Noether charge of translations along the trajectories of the modular flow, and determine the local temperature as seen by an observer that moves along these trajectories.
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Cited by 3 Pith papers
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Petz-R\'enyi relative entropy in QFT from modular theory
Petz-Renyi relative entropy for coherent excitations of free quantum fields is computed from modular theory and shown to involve the symmetric part of the two-point function, unlike relative entropy.
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Relative entropy of vacuum vs coherent state for λφ⁴ in the Rindler wedge equals the classical interacting boost charge to O(λ) and obeys the Bekenstein bound.
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A numerical analysis of Araki-Uhlmann relative entropy in Quantum Field Theory
For a free massive scalar field in 1+1 dimensions, the Araki-Uhlmann relative entropy between a coherent state and the vacuum decreases with mass and increases with region size in numerical tests.
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