We discuss how to define a kinematical horizon entropy on a causal set. We extend a recent definition of horizon molecules to a setting with a null hypersurface crossing the horizon. We argue that, as opposed to the spacelike case, this extension fails to yield an entropy local to the hypersurface-horizon intersection in the continuum limit when the causal set approximates a curved spacetime. We then investigate the entropy defined via the spacetime mutual information between two regions of a causal diamond truncated by a causal horizon, and find it does limit to the area of the intersection.

中文翻译：

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在因果集的视界熵

我们讨论如何在因果集上定义运动视界熵。我们将最近对视界分子的定义扩展到具有零超曲面穿过视界的设置。我们认为，与类空间情况相反，当因果集接近弯曲时空时，这种扩展无法在连续极限中产生局部于超曲面-水平交点的熵。然后，我们研究了由因果视界截断的因果钻石的两个区域之间的时空互信息定义的熵，并发现它确实限制在交叉点的区域内。