发表机构
Institute of Theoretical Physics, Dalian University of Technology（大连理工大学理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究在CCKLP–Witten框架下，于GUE模型中推导原面积熵第一定律，明确其响应系数含普适因子1/3，系数参数匹配半经典关系，为全息纠缠楔重建提供关键结果。
AI 中文摘要
我们在CCKLP–Witten框架下推导了近似全息纠缠楔重建中的原面积熵第一定律。中心谱函数具有核为$L(x)=x\tanh(x/2)$的模哈密顿量表示。对于近极大混合的体态，且在编码微扰的非结构化高斯幺正系综（GUE）模型内，系综平均的原面积熵与体熵在领头阶呈线性变化，响应系数包含一个普适因子$1/3$，该因子源于$L''(0)/2=1/6$，且在该模型内与体谱的具体形状无关。施加非零反作用所需的引力标度条件后，第一定律系数为$O(1)$，参数上与半经典关系$\frac{\rm Area}{4G_N}=\frac{\rm \bf \text{δ}}{\rm \bf \text{δ}}S_{\rm bulk}$匹配。
英文摘要
We study how much of the proto-area response can be inferred from the bulk von Neumann entropy. In the perturbative holographic code setting considered by CCKLP and Witten, we keep the recovery frame fixed and analyze the response averaged over the GUE at second order in the encoding perturbation. Near the maximally mixed bulk spectrum, the response is fixed by the entropy through quadratic order. For $d_1\geq3$, spectral information first enters at cubic order through the third centered moment, so states with the same entropy can have different responses. We determine the resulting response range on small equal-entropy level sets and obtain its sharp leading $D^{3/2}$ dependence, including the coefficient. The corresponding minimax error for prediction from entropy alone is one half of this range. For $d_1=2$, the entropy instead determines the response exactly.
Commentsv2: Revised version with strengthened results and improved discussion of equal-entropy ambiguity
