How to Measure the Chaos of Spacetime Itself ⚡ экспресс
Relying on the Landauer principle (the connection between information erasure and heat release), the authors construct a geometric measure of entropy for static spherically symmetric spacetime. By considering a family of geodesics (free-fall paths) through a surface, entropy is defined as a surface integral of the entropies of individual geodesics. Under mild conditions, the second law is proved for this 'Landauer entropy', and it is linked to the Bekenstein–Hawking entropy. Much like the pattern of fountain jets carries information about pressure, the distribution of geodesics encodes the entropy of the gravitational field. This is a step toward merging thermodynamics and geometry.
Spacetime isn't a flat sheet, but a crumpled fabric: stars and planets leave creases on it. Information is written into every crease, and to erase it, heat would have to be released — that's how Landauer's principle works. Thus, the 'crumpledness' of space can be measured through entropy — the universal measure of disorder.
Physicists passed a bunch of light rays through a curved region — like threads through a wrinkled patch. Each ray brings a share of chaos, and their total sum gives the entropy of the whole geometry. For a non-rotating black hole, this count leads to the legendary formula of Bekenstein and Hawking: S = A/4, where A is the horizon area. The most surprising thing: no matter what falls into the hole, its entropy increases only due to the growth of the surface area, not because of the absorbed matter. It's as if space itself remembers only how much room it took up.
Thus, from a passive background, space turns into an active player, weaving gravity, information, and heat into a single tangle.
🎯 A black hole doesn't care what falls into it: two objects with different internal entropies, when swallowed by the hole, will increase its entropy by the same amount — solely due to the horizon's growth.