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From the Beckenstein-Hawking formula, we know that entropy is proportional to the area of the event horizon of a black-hole: $S\propto A$.

From Loop Quantum Gravity, we know that length, area and volume are quantized.

So, does it mean that entropy is also quantized?

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    $\begingroup$ From Loop Quantum Gravity, we know that length, area and volume are quantized. Is this statement actually experimentally verified? $\endgroup$
    – BioPhysicist
    Commented Jan 21, 2019 at 12:39
  • $\begingroup$ @AaronStevens LQG predicts that length, area and volume are quantized. Is it better? $\endgroup$
    – mattiav27
    Commented Jan 21, 2019 at 12:45
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    $\begingroup$ Are you asking, "In a world where loop quantum gravity is true, is entropy quantized?" or are you asking, "Do we have any evidence that entropy is quantized, as loop quantum gravity would suggest?" $\endgroup$
    – probably_someone
    Commented Jan 21, 2019 at 14:13
  • $\begingroup$ @probably_someone I am asking "In a world where loop quantum gravity is true, is entropy quantized?" $\endgroup$
    – mattiav27
    Commented Jan 21, 2019 at 14:22

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I found this overview which in the abstract talks about "effective quantization of entropy" in loop quantum gravity. As entropy is a variable depending statistically on the number of microstates in a given macrostate, it is obvious that the term "quantization" can be only effectively used.

In section V they explore with a computer the number of states that would define the entropy and find :

What one notes is that the entropy has a completely different behavior for this particular choice of interval: Instead of oscillations, the entropy seems to increase in discrete steps. Furthermore, the height of the steps seems to approach a constant value as the area of the horizon grows, thus implementing in a rather subtle way the conjecture by Bekenstein that entropy should be equidistant for large black holes. Quite remarkably, this result is robust, namely, it is independent of the counting.

It goes on to analyze further and show enhancements on the black hole area that can explain the behavior.

So it is an effective quantization of entropy, a statistical result of the quantization behavior of the area under consideration.

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