2026-10-26 · arXiv Quantum Physics
arXiv:2610.31680v1 Announce Type: cross
Abstract: R\'enyi entropy inequalities have been proposed to strengthen the area-theorem bound on mergers of thermodynamically stable black holes in Anti de Sitter (AdS) space. The stronger bounds depend on the joint initial state, whereas masses and temperatures fix only its local thermal marginals. We quantify this distinction inside the canonical two-hole description. Correlations confined to rare energy fluctuations can leave both thermal states exactly intact and drive the trace distance and mutual information to zero, yet still change the joint R\'enyi entropy at leading semiclassical order. We determine the smallest entropy compatible with a controlled approach to statistical independence, uniformly over all positive R\'enyi orders up to one. For equal Schwarzschild--AdS$_4$ holes, the resulting optimized canonical mass constraint reduces to the area bound at leading semiclassical order. The reduction concerns only the information needed to infer a bound; it does not produce a lighter attainable remnant or a dynamical instability. Stronger merger constraints therefore require control of the initial correlations beyond single black hole thermodynamics.
原文链接：https://arxiv.org/abs/2610.31680
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