标题： 信息内容和最小长度度量：一滴光 显示英文标题

标题： Information content and minimum-length metric: A drop of light

摘要： 在大量将引力与热力学、统计学、信息联系起来的结果中，描述了一条尝试从引力场的(非)局域性角度探索这种联系的路径。 首先强调的是，与零超曲面（即光线片和广义协变熵界限）相关的著名热力学结果可以被解释为暗示引力的不可约内在非局域性。 即使这种非局域性可能在普通尺度上被掩盖（取决于哪种物质是引力场的源，以及我们用哪种物质来探测后者），它不可避免地在最小尺度上显现出来，即普朗克长度$l_p$，无论我们考虑何种情况。 然后探讨了这种非局域性在赋予时空本身以最小长度$L$时所带来的后果，特别是众所周知且引人入胜的事实，即这使得场方程以及整个引力作为统计力学的结果出现。 在这里，通过从一个假想的（在普通时空中的）一般事件周围通过光线片来探测（而不是像其他叙述中那样通过类空或类时测地线族）。 这些推导的工具是非局域量，其中最小长度的里奇标量尤为突出，因为它既为引力的统计描述提供了微观自由度，又因为有趣的是，在$L\to 0$极限下无法从中恢复普通的或“经典”的里奇标量。 强调的是，这种方式通常会得到经典引力，但对于$\hbar\ne 0$而言，不是在$\hbar\to 0$极限下（统计推导的场方程在此极限下变得奇异），这补充了这一方面的先前结果。 （摘要截断；详见论文中的完整摘要） 显示英文摘要

摘要： 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 $L\to 0$ limit. Emphasis is put on that classical gravity is generically obtained this way for $\hbar\ne 0$, but not in the $\hbar\to 0$ limit (the statistically derived field equations become singular in this limit), adding to previous results in this sense. (truncated Abstract; see the paper for full Abstract)