Concept
Entropy & Black Hole Entropy
Pronounced: EN-truh-pee
Entropy is a measure of disorder that never decreases. Its surprising connection to black holes, the Bekenstein-Hawking entropy, was one of Hawking's deepest contributions.
Last updated 23 May 2026 · How we research
Entropy is a measure of disorder, or more precisely of the number of ways the parts of a system can be arranged. The second law of thermodynamics says that the total entropy of an isolated system never decreases: things tend from order toward disorder, which is why a smashed cup never reassembles itself. Entropy is also closely tied to the arrow of time, the reason the past and future feel so different.
The black hole connection
The remarkable twist, and one of Hawking's most important contributions, is that black holes have entropy too. In the early 1970s the physicist Jacob Bekenstein noticed that the area of a black hole's event horizon behaves just like entropy: Hawking had proved it can never decrease, exactly as entropy never decreases. Bekenstein proposed that a black hole's entropy really is proportional to its surface area.
Hawking at first disagreed, but his own work on Hawking radiation ended up proving Bekenstein right and fixing the exact relationship, now called the Bekenstein-Hawking entropy. The implication is profound: it means a black hole's entropy is written on its two-dimensional surface rather than hidden in its volume, a clue that led to the holographic principle and remains central to the search for a theory of quantum gravity.
Explore how entropy scales with horizon area in the entropy visualiser.
The mathematics, gently
The entropy of a black hole is given by the Bekenstein-Hawking formula:
S = k_B c³ A / (4 G ħ)
The remarkable thing is that the entropy depends on the area A of the event horizon, not the volume. This is the seed of the holographic principle: the idea that the information content of a region can be encoded on its boundary. It also means a black hole has more entropy than anything else of comparable size, which is why merging black holes always increases total entropy, in line with the second law of thermodynamics.