In the vast amount of results linking gravity with thermodynamics, statistics, information, a path is described which tries to explore this connection from the point of view of (non)locality of the gravitational field. First the emphasis is put on that well-known thermodynamic results related to null hypersurfaces (i.e. to lightsheets and to generalized covariant entropy bound) can be interpreted as implying an irreducible intrinsic nonlocality of gravity. This nonlocality even if possibly concealed at ordinary scales (depending on which matter is source of the gravitational field, and which matter we use to probe the latter) unavoidably shows up at the smallest scales, read the Planck length \(l_p\), whichever are the circumstances we are considering. Some consequences are then explored of this nonlocality when embodied in the fabric itself of spacetime by endowing the latter with a minimum length L, in particular the well-known and intriguing fact that this brings to get the field equations, and all of gravity with it, as a statistical-mechanical result. This is done here probing the neighborhood of a would-be (in ordinary spacetime) generic event through lightsheets (instead of spacelike or timelike geodesic congruences as in other accounts) from it. The tools for these derivations are nonlocal quantities, and among them the minimum-length Ricci scalar stands out both for providing micro degrees of freedom for gravity in the statistical account and for the fact that intriguingly the ordinary, or ‘classical’, Ricci scalar can not be recovered from it in the \(L\rightarrow 0\) limit. Emphasis is put on that classical gravity is generically obtained this way for \(\hbar \ne 0\), but not in the \(\hbar \rightarrow 0\) limit (the statistically derived field equations become singular in this limit), adding to previous results in this sense. This hints to that the geometric description of gravity we are used to is intrinsically quantum, as it requires \(\hbar \ne 0\), on top of being of statistical-mechanical origin. One would expect that this inherently non-classical nature might show up through nonlocality also at scales much larger than \(l_p\) if special suitable circumstances are considered.

在将引力与热力学、统计学、信息联系起来的大量结果中，描述了一条路径，试图从引力场的（非）局部性的角度来探索这种联系。首先，重点放在与零超表面（即与光片和广义协变熵界）相关的众所周知的热力学结果可以解释为暗示不可约的固有非定域性。这种非定域性即使可能隐藏在普通尺度上（取决于哪种物质是引力场的来源，以及我们使用哪种物质来探测后者）不可避免地会在最小尺度上出现，请阅读普朗克长度\(l_p\)，以我们正在考虑的情况为准。然后通过赋予时空结构最小长度L来探索这种非定域性在时空结构本身中的一些后果，特别是众所周知且有趣的事实，它带来了场方程，以及所有的重力，作为统计力学结果。这是在这里完成的，通过光片（而不是像其他帐户中的类空间或类时测地线全等）从中探测可能（在普通时空中）通用事件的邻域。这些推导的工具是非局部量，其中最小长度的 Ricci 标量在统计帐户中为重力提供微自由度以及有趣的是普通或“经典”Ricci 标量可以在\(L\rightarrow 0\)限制内无法从中恢复。强调经典引力一般是通过这种方式获得的\(\hbar \ne 0\)，但不在\(\hbar \rightarrow 0\)限制中（统计导出的场方程在此限制中变得奇异），在这个意义上增加了先前的结果。这暗示我们习惯于对引力的几何描述本质上是量子的，因为它需要\(\hbar \ne 0\)，并且是统计力学起源的。如果考虑到特殊的合适情况，人们会期望这种固有的非经典性质可能会通过非定域性出现在比\(l_p\)大得多的尺度上。