Ergodic Equilibration of Rényi Entropies and Replica Wormholes

Abstract

We study the behavior of Rényi 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 Rényi 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.

23 pages, 4 figures

References in corpus (4)

• Holographic Evolution of Entanglement Entropy
• Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space
• Statistical distribution of quantum entanglement for a random bipartite state
• Hints of Gravitational Ergodicity: Berry's Ensemble and the Universality of the Semi-Classical Page Curve

Cited by in corpus (5)

• Wormholes from heavy operator statistics in AdS/CFT
• Islands in the Stream of Hawking Radiation
• Grey-body Factors, Irreversibility and Multiple Island Saddles
• Bootstrapping Quantum Extremal Surfaces I: The Area Operator
• The entanglement entropy of typical pure states and replica wormholes