发表机构
University of Houston（休斯顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为闵可夫斯基时空中的因果菱形视界建立统一热力学框架，导出温度、熵-面积关系及局域第一、第二定律，并证明其视界定律结构在任意维度成立。
AI 中文摘要
我们在闵可夫斯基时空中为因果菱形视界建立了一个统一的热力学与力学框架。欧几里得正则性确定了温度 $T_D=1/(\pi\alpha)$，其中 $2\alpha$ 是菱形的时域范围。经调节的吉本斯-霍金-约克贡献给出 $I_D^E=-A_0/(4G)$，其中 $A_0$ 是视界分叉面的面积，而平衡几何能量为零则导出了熵-面积关系 $S_D=A_0/(4G)$。对于穿越未来视界局部区域的弱物质扰动，Raychaudhuri 分析将相关的 Killing 能量通量与面积响应联系起来，在分叉面附近的一阶近似下得到一个局域物理过程第一定律，并且对于满足零能量条件的经典物质，还得到一个局域第二定律。均匀共形表面引力确立了第零定律，而零温度仅在 $\alpha\to\infty$ 极限下趋近，此时有限因果视界消失。这些结果表明，在因果菱形（闵可夫斯基时空因果结构的基本构建块）内可以出现一致的视界定律结构。该推导在 $(2+1)$ 维中是显式的，而物理结果对于 $d\geq3$ 维中的球形因果菱形保持相同形式。
英文摘要
We develop a unified thermodynamic and mechanical framework for causal-diamond horizons in Minkowski spacetime. Euclidean regularity fixes the temperature $T_D=1/(πα)$, where $2α$ is the temporal extent of the diamond. The regulated Gibbons--Hawking--York contribution gives $I_D^E=-A_0/(4G)$, with $A_0$ the area of the horizon bifurcation surface, and the vanishing equilibrium geometric energy then yields the entropy--area relation $S_D=A_0/(4G)$. For weak matter perturbations crossing a localized portion of the future horizon, a Raychaudhuri analysis relates the associated Killing-energy flux to the area response, yielding a local physical-process first law at leading order near the bifurcation surface and, for classical matter satisfying the null energy condition, a local second law. Uniform conformal surface gravity establishes the zeroth law, while zero temperature is approached only in the limit $α\to\infty$, in which the finite causal horizon disappears. These results show that a coherent horizon-law structure can arise within a causal diamond, a fundamental building block of the causal structure of Minkowski spacetime. The derivation is explicit in $(2+1)$ dimensions, while the physical results retain the same form for spherical causal diamonds in $d\geq3$.
