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arXiv · 2103.09880

Ergodic Equilibration of R\'enyi Entropies and Replica Wormholes

Martin Sasieta
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Abstract

We study the behavior of R\'enyi entropies for pure states from standard assumptions about chaos in the high-energy spectrum of the Hamiltonian of a many-body quantum system. We compute the exact long-time averages of R\'enyi entropies and show that the quantum noise around these values is exponentially suppressed in the microcanonical entropy. For delocalized states over the microcanonical band, the long-time average approximately reproduces the equilibration proposal of H. Liu and S. Vardhan, with extra structure arising at the order of non-planar permutations. We analyze the equilibrium approximation for AdS/CFT systems describing black holes in equilibrium in a box. We extend our analysis to the situation of an evaporating black hole, and comment on the possible gravitational description of the new terms in our approximation.

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Martin Sasieta. 2021-03-17. Ergodic Equilibration of R\'enyi Entropies and Replica Wormholes. https://doi.org/10.1007/jhep08(2021)014

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