2025/01/20 by Minghui Yu, Yu, Ming-Hui, Shu-Yi Lin +3 · 4 citations
Earth and Planetary Sciences · Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geophysics and Gravity Measurements #High Energy Physics - Theory (hep-th) #Pulsars and Gravitational Waves Research #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2501.11474
openalex publication_date 2025/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
By employing the replica trick we study the impact of the replica parameter n on the modular entropy and the capacity of entanglement in the End of the World (EoW) model and the island model, respectively. For the EoW model, we present n-dependent evolution curves of the modular entropy and the capacity of entanglement under both microcanonical and canonical ensembles. In particular, in the canonical ensemble, all quantities decrease as n increases at late times. For the island model, we develop the replica geometry for finite n and re-evaluate the modular entropy and the capacity of entanglement in a two-sided eternal Jackiw-Teitelboim black hole coupled with a thermal bath. In the case of a single island configuration, the modular entropy and capacity of entanglement closely resemble the thermal entropy and the heat capacity, respectively, yielding results analogous to those obtained in the canonical ensemble for the EoW model. The analysis of the results from these two models strongly indicates that in geometries with a greater number of n copies, more connected geometries effectively purify thermal Hawking radiation. In addition, we compare these findings with statistical mechanics and provide an interpretation for the replica parameter n. Finally, we generalize the island formula to accommodate the finite n case under this interpretation.