How to Measure the Chaos of Spacetime Itself ⚡ экспресс
Based on the Landauer principle, a geometric definition of entropy for static spherically symmetric spacetime is introduced. A congruence of geodesics passing through a surface is studied; the entropy of the congruence is computed as a surface integral of the entropies of its constituent geodesics. Under certain mild assumptions, the second law of thermodynamics is proved for the resulting function (dubbed Landauer entropy). The connection between this entropy and the well-known Bekenstein–Hawking entropy is shown. The work demonstrates how principles of information theory can be embedded into general relativistic geometry, offering a universal measure of entropy for curved spacetime.
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.