发表机构
Nanjing University of Aeronautics and Astronautics（南京航空航天大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在Jacobson的热力学推导基础上，对比GEVAG与EGC框架的异同，研究其对贝肯斯坦界的影响，最终提出实验室测量的$G$本质的核心问题。
AI 中文摘要
在Jacobson从热力学推导爱因斯坦场方程的基础上，本文提出了“广义熵与变G”（GEVAG）框架，该框架将广义视界熵$S=f(A)/4G$一致地融入时空的热力学与几何中，由此得到有效引力耦合常数$G_\text{eff}=G/f'(A)$。相关的“熵-引力对应”（EGC）则等价于将该视界关系提升为径向变化的体耦合$G_\text{eff}(r)$。我们阐明了这些方法之间的相似性与根本区别：尽管它们共享相同的视界一致性关系，但其整体因果结构与渐近几何却可能存在显著差异；此外，EGC的径向规定会为多中心构型引入额外的模糊性。我们进一步研究了GEVAG的近视界扩展，该扩展恢复了仅视界表述中缺失的热力学质量与ADM质量的等价性，随后讨论了这些不同规定对贝肯斯坦界（Bekenstein bound）的影响。贝肯斯坦界在近视界GEVAG、EGC以及近期通过Wald熵重建广义熵几何的$f(R)$重构方法中得到的$G_\text{eff}$之间建立了令人惊讶的联系。最后，我们提出了最重要的问题：实验室中测量的$G$究竟是什么？
英文摘要
Building on Jacobson's thermodynamics derivation of Einstein field equations, the "generalized entropy and varying-G" (GEVAG) framework was proposed to consistently incorporate generalized horizon entropy $S=f(A)/4G$ into both the thermodynamics and the geometry of spacetime. This leads to an effective gravitational coupling $G_\text{eff}=G/f'(A)$. A related "entropy-gravity correspondence" (EGC) instead is equivalent to promoting this horizon relation to a radially varying bulk coupling $G_\text{eff}(r)$. We clarify the similarities and fundamental distinctions between these approaches. Although they share the same horizon consistency relation, their global causal structures and asymptotic geometries can differ substantially. In addition, the radial prescription of EGC introduces an additional ambiguity for multi-center configurations. We further examine a near-horizon extension of GEVAG, which restores the equivalence between thermodynamic and ADM masses that is absent in the horizon-only formulation. We then discuss the implications of these different prescriptions for the Bekenstein bound. The Bekenstein bound provides a surprising link between $G_\text{eff}$ in near horizon GEVAG, EGC, and the one obtained in the recent $f(R)$-reconstruction approach of generalized entropy geometry via Wald entropy. Finally, we raise the most important question: what exactly is the $G$ measured in laboratories?
