Where did the idea of a connection between information and area come from? In the 1970s, Stephen Hawking and Jacob Bekenstein pondered: if you throw a cup of hot tea into a black hole, the tea's entropy would disappear, and the total entropy of the Universe would seemingly decrease—violating the second law of thermodynamics. The solution came from calculations: a black hole's entropy must be proportional to the area of its event horizon (the surface from which nothing can escape). Bekenstein went further: he hypothesized that any physical system contained within a sphere of radius R with energy E cannot have an entropy greater than that of a similar sphere that had collapsed into a black hole. Thus the Bekenstein bound was born—a bridge between gravity, thermodynamics, and information theory. This bound is like a rule: no matter how many books you place on a shelf, their total ‘story capacity’ cannot exceed the throughput of the door to the room. The door here is the surface area.
History
The theorem was proposed by Jacob Bekenstein in 1981 (Physical Review D, 23, 287). By then Bekenstein was already known as the originator of black hole entropy (1972). The initial impetus came from a thought experiment: if you lower an entropy-bearing object into a black hole, its horizon must increase just enough to compensate for the loss of entropy from the outside world; otherwise, the second law of thermodynamics would be violated. Generalizing, Bekenstein derived a limit for any system, not necessarily one collapsing into a hole. Later the bound was corroborated within the framework of quantum information theory and the holographic principle of 't Hooft and Susskind.
How it works
The Bekenstein bound is actively used in black hole physics, quantum gravity, and quantum information theory. For black holes it is saturated—their entropy equals exactly A/(4ℓ_P²), where A is the horizon area, ℓ_P the Planck length. For ordinary macroscopic bodies the bound is astronomically large and not reached; for example, for a liter of water it amounts to about 10⁶⁵ bits, many orders of magnitude greater than the actual physical entropy. Practical applications are still limited, but the bound sets fundamental limits for quantum computers and data storage density.
In practice
This limit determines how much data can be stored in quantum computers and explains why black holes are the most capacious information stores in the Universe.
Fun fact
The Bekenstein bound for the human brain is about 10⁷⁰ bits. That's billions of times more than all data ever stored by humanity. So our brain is still far from saturation, even though it operates on classical, not quantum, principles.
A black hole is a maze with no way out. But what happens to the information inside? To test this, physicists didn't fly to the nearest hole; instead, they built a tiny replica on a quantum processor. The maze was played by a chain of 32 superconducting qubits, where each step leads only forward, like a one-way corridor.
A courier delivers packages to a building with two entrances. While the door is open, he freely enters both. But once one door starts to close, getting inside becomes harder and harder. That's roughly how information behaves at a black hole's horizon — the invisible boundary from which nothing can escape.
In the new study, scientists described this process as two opposing flows.
Stare long enough into the night sky, and sooner or later your gaze hits a blackness beyond which nothing is visible. This is not just a distant fence: it is the edge of the universe accessible to us, the cosmic horizon. Light from more distant stars simply hasn't had time to reach us.
A black hole is not just a dark spot in space. It has a temperature, and it radiates. It has entropy — a measure of hidden information encoded on its horizon's surface, like a pattern on a soap bubble.
A black hole has three laws, just like an ideal gas. The first: energy is conserved. The second: the horizon area never decreases. And the third, the most finicky, demands that at zero temperature the entropy (a measure of disorder) tend to zero or a universal constant.
A black hole has three laws, just like an ideal gas. The first: energy is conserved. The second: the horizon area never decreases. And the third, the most finicky, demands that at zero temperature the entropy (a measure of disorder) tend to zero or a universal constant.
A fussy thermometer shows different temperatures depending on who is looking at it. A black hole behaves much the same way: its thermal properties, entropy and temperature, depend on how we describe the information hidden inside.
In the far reaches of space, there exists a hypothetical object: an ultracold black hole. It is charged and resides in an expanding universe (de Sitter space). Its temperature hovers just above absolute zero — about one trillionth of a degree above it.
A black hole is not just an abyss. It is a seething cauldron whose temperature rises as it evaporates. The authors of the study found that when the heat reaches a critical threshold, the hole seems to boil. It emits superheavy particles — the very ones that exist on a scale where any theory of gravity collapses.
The quantum vacuum is not empty: it is permeated by entanglement linking distant regions. But when physicists tried to compute this entanglement, it turned out to be infinite. The culprit: particles with very low energy that can smear out over arbitrarily large volumes. They are like waves with no shores to contain them.
Imagine a factory capable of producing a million parts per hour, yet it only makes a hundred. That's roughly how our Universe behaves when viewed through the lens of entropy — a measure of disorder that, according to physics, must only increase. The main "machines" of this factory are supermassive black holes.
A black hole devours everything, even light. Yet it obeys the laws of physics: it possesses entropy — a measure of the hidden information an object 'remembers.' In the 1970s, Jacob Bekenstein and Stephen Hawking discovered a strange pattern: a black hole's entropy grows not with its volume, but…
In 1973, Jacob Bekenstein proposed that black hole possess entropy — a measure of hidden disorder. Stephen Hawking later confirmed this by adding radiation, but the microscopic origin of entropy remained obscure.
A climber on a ridge notices something strange: the horizon around them seems to freeze. No forward, no backward — only emptiness and silence. This is roughly the picture painted by new calculations for our Universe. At some point in its expansion, the invisible boundary, the future event horizon, stopped growing.
An engineering blueprint of a skyscraper always includes a number: the maximum load on the foundation — say, 500 kilopascals. Einstein's field equations in curved spacetime impose a similar limit on the 'force load' inside stars, planets, and any other clumps of matter.
An engineering blueprint of a skyscraper always includes a number: the maximum load on the foundation — say, 500 kilopascals. Einstein's field equations in curved spacetime impose a similar limit on the 'force load' inside stars, planets, and any other clumps of matter.
A light ray skimming along a black hole horizon doesn't just move: it carries heat and information. Physicists have long suspected that the geometry of such rays obeys strict rules, but the details remained blurry. The new work turns these rules into a sharp inequality.
A Tesla coil crackles, and a beam of light begins to rotate around it. The medium it passes through is still stable, but the field grows, and the rotation intensifies. This is not a trick but the behavior of special materials that couple electricity and magnetism. For such coupling, there is a fundamental limit — the Tellegen limit.
A quantum computer relies on two forces: entanglement (particles behaving as a single whole) and "magic"—a measure of how far a state is from familiar classical physics. But how these two resources relate as a many-particle system evolves in time has remained a puzzle.
The authors approached the problem through time.
The cosmological horizon — the edge of the observable Universe, which is expanding at an accelerating rate — is like a safe with a timer. Information about what crosses this boundary doesn’t vanish but returns, albeit with a delay. Physicists have figured out how long this pause lasts.
A black hole is not just a vacuum cleaner. It glows faintly, emitting particles — this idea was proposed by Jacob Bekenstein, who connected the hole's temperature to its degree of disorder. Detecting such radiation in space is incredibly difficult.
A black hole resembles a safe that slowly gives up its contents, energy and information, through a faint glow known as Hawking radiation. But if the safe opens too quickly, a 'firewall' may flare up at its boundary — a region where the familiar laws of physics break down.
In the new work, physicists complicated the model of this safe.
The black hole paradox has haunted physicists for decades. If a hole evaporates, where does its contents go? Discoveries by Stephen Hawking and Jacob Bekenstein showed that saving the laws of nature requires an unconventional move.
Imagine the universe as a woven blanket of invisible threads.
Our universe is expanding, and its future, according to cosmologists, is empty, cold de Sitter space. Understanding its quantum nature is like trying to read a book by looking only at its cover. The holographic principle suggests that all information about what happens inside a volume can be encoded on its boundary, like a picture on a film.
Erasing even a single bit means releasing heat. This discovery by Rolf Landauer hinted that information is neither material nor illusory. Imagine that every event casts a shadow: that is information, the collection of all unrealized possibilities.
Space is like a sheet of paper: gravity bends it, making lines converge toward the center. But if you bend too hard, the paper tears, just as space, under monstrous curvature, doesn't collapse into a point but forms a torn edge. That edge is the quantum boundary.
A pot of water always boils the same way: hit 100 degrees and bubbles start. Quantum fluids are different. When a cloud of atoms is cooled to near absolute zero, it can turn into a single matter wave — a Bose–Einstein condensate. But the transition itself, it turns out, can happen in three different ways.
If you toss a book into a black hole, the pages don't vanish without a trace: their content remains encoded in the radiation the hole emits. But how exactly does that happen? In some models, 'islands' appear — regions inside the hole that seem to push information back out.
Immediately after the Big Bang, space may have vibrated like a string from quantum effects. As these oscillations faded, they would have left a mark on the expansion of galaxies — a memory effect. The search for this echo in telescope data turned up nothing.
Spacetime is like a giant sheet of paper. Fold it, and distant corners come together. Poke a pencil through, and you get a wormhole, a short tunnel through the folds. But the paper wants to spring back flat, snapping the passage shut. To keep it open, you need a rare “gasket”—matter with negative energy.
A light beam approaches a black hole not head-on, but at a glancing angle. If the angle is just right, the light neither falls in nor escapes: it starts looping around, like a figure skater circling the rim of a funnel. This narrow track is the photon ring. It acts like a lens, repeatedly reflecting the image of everything that falls into the hole.
An acoustic black hole is a fluid flow faster than sound, so sound waves can't escape. The boundary, the surface where the flow speed reaches the speed of sound, spawns pairs of phonons: sound quanta, one flying away, the other plunging inward.
A soap bubble hangs in the air, and its shape already contains everything needed to calculate the internal tension. A similar principle worked in a new study on quantum gravity. Physicists took a closed surface, an analog of such a bubble, and specified a few numbers on it: for example, the electric field strength and the curvature.
The universe is filled with invisible dark matter. Just as a drop of water, as it evaporates, leaves behind a tiny salt crystal, so too can a black hole evaporate, leaving behind a minuscule stable remnant.
Drop a handful of sand into calm water — the ripples spread and fade. Drop it into a running blender — the vortices mix everything in an instant. Physics has a similar rule: chaos cannot grow faster than a certain rate.
A black hole is like a perfect safe: anything that goes in seems lost forever. But at the microscopic level, it doesn't destroy information: it shuffles it with its internal degrees of freedom, much like a deck of cards after a thorough shuffle.
Light falling into a black hole carries information — for instance, the path a photon took. The horizon (the surface from which nothing returns) responds by changing its entropy — a measure of disorder, akin to the number of shuffled pages in a book.
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.
