Light Sheets and Bekenstein's Entropy Bound

From the covariant bound on the entropy of partial light sheets, we derive a version of Bekenstein’s bound: S/M≤πx/ℏ, where S, M, and x are the entropy, total mass, and width of any isolated, weakly gravitating system. Because x can be measured along any spatial direction, the bound becomes unexpectedly tight in thin systems. Our result completes the identification of older entropy bounds as special cases of the covariant bound. Thus, light sheets exhibit a connection between information and geometry far more general, but in no respect weaker, than that initially revealed by black hole thermodynamics.