Second law of black hole thermodynamics

If simple entropy in the Bekenstein-Hawking area law for a Schwarzschild black hole is replaced with 'negative' quantum conditional entropy, which quantifies quantum entanglement, of positive-energy particles of the black hole relative to its outside, a paradox with the original pair-creation picture of Hawking radiation, the first law for black hole mechanics and quantum mechanics is resolved. However, there was no way to judge experimentally which area law is indeed adopted by black holes. Here, with the no-hair conjecture, we derive the perfect picture of a second law of black hole thermodynamics for any black hole from the modified area law, rather than Bekenstein's generalized one from the original area law. The second law is testable with an event horizon telescope, in contrast to Bekenstein's. If this is confirmed, the modified area law could be exalted to the first example of fundamental equations in physics which cannot be described without the concept of quantum information.