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Replica wormholes and capacity of entanglement
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We consider the capacity of entanglement as a probe of the Hawking radiation in a two-dimensional dilaton gravity coupled with conformal matter of large degrees of freedom. A formula calculating the capacity is derived using the gravitational path integral, from which we speculate that the capacity has a discontinuity at the Page time in contrast to the continuous behavior of the generalized entropy. We apply the formula to a replica wormhole solution in an eternal AdS black hole coupled to a flat non-gravitating bath and show that the capacity of entanglement is saturated by the thermal capacity of the black hole in the high temperature limit.
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Replica Wormholes, Modular Entropy, and Capacity of Entanglement in JT Gravity
In JT gravity toy models, late-time modular entropy and capacity of entanglement scale inversely with n times the inverse temperature, supporting a thermal reading of the replica parameter.
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