I must be very high entropy. I got up very early today after too little time in bed, much less asleep and it’s comfy warm in the house. Close to zero energy is available for useful work.
I’ll read the rest of the thread seriously after my nap when my entropy is lower. 
In the interest of fighting ignorance, and after further reflection, I concede this point. Shannon entropy is not relevant to expressing the information content of a flash drive. Kolmogorov complexity is the appropriate metric. (There is no metric at all for expressing the “information content” of a human brain.)
I think a bit of clarification all around is needed here. I first brought up “homogeneity” in my first reply in the context of structural organization, but then added in the next post that with respect to thermodynamic entropy, gravity typically acts in exactly the way you describe, reducing local entropy by heating infalling matter and thus increasing the temperature differential between the aggregated mass and the area outside, which then gets radiated away.
However, things are quite different when a black hole forms, mainly because, except for interactions at the event horizon, the thermal energy from infalling mass cannot get radiated away. I found it interesting that the entropy of a black hole as observed from outside is described by the Bekenstein-Hawking entropy and in particular by its formulation of the “Generalized Second Law” of thermodynamics. Two implications are of note here. The first is that matter falling into a black hole increases its entropy, and this increase exceeds the entropy that disappears beyond the event horizon. The second is that the entropy of a black hole is very large indeed. The calculations show that a one-solar mass Schwarzschild black hole has a thermodynamic entropy about 20 orders of magnitude larger than the sun.
This great increase in entropy can be rationalized as due to the tremendous loss of information as the original matter collapses to form the black hole. Whether it’s appropriate to represent this as “homogenization” is rather a semantic quibble, but it seems reasonable as the only visible attributes are now mass, spin, and charge and nothing else. What is beyond the event horizon is unknowable and doesn’t concern us.
Yes, that’s what I was talking about above when I said that a BH is a maximum-entropy object.
However, I’m not sure that’s the best way to think about it. The way I always heard it, from classical general relativity, you should expect black holes to be very low-entropy object, as their state—the total state, not just the macrostate—is exhaustively described by the three quantities you mention; hence, there is only one state for the black hole to occupy, leaving its entropy minimal. This is also the way Johnathan Oppenheim tells the story in his Nature Physics-obituary on Jacob Bekenstein:
A black hole, on the other hand, has no entropy according to general relativity, being uniquely described by macroscopic quantities such as mass, angular momentum and electric charge. This, Bekenstein dubbed ‘the no-hair theorem’.
This also jibes with the fact that the entropy of a cloud of gas under the influence of gravity goes as the log of its volume, thus decreasing as it collapses. Furthermore, it’s the basis of the well-known black hole information paradox: Hawking calculated that the outgoing radiation would depend only on the black hole’s mass, charge, and angular momentum, having a thermal spectrum. thus failing to preserve the information of whatever went into the black hole.
However, looking around, there are some views similar to yours, e. g. here:
A stationary black hole is parametrized by just a few numbers (Ruffini and Wheeler 1971): its mass, electric charge and angular momentum (and magnetic monopole charge, except its actual existence in nature has not been demonstrated yet). For any specific choice of these parameters one can imagine many scenarios for the black hole’s formation. Thus there are many possible internal states corresponding to that black hole. In thermodynamics one meets a similar situation: many internal microstates of a system are all compatible with the one observed (macro)state. Thermodynamic entropy quantifies the said multiplicity. Thus by analogy one needs to associate entropy with a black hole.
It would seem to me that these microstates aren’t accounted for by general relativity, however, so such a view seems speculative on that front. As far as I know, the first detailed microscopic account of the black hole entropy was given by the ‘fuzzball’ proposal in string theory, then a much-touted ‘success’ positing it as a viable theory of everything.
But that’s beyond my area of expertise, so take it with a grain of salt. Perhaps somebody better versed in GR (@Asympotically_fat, @Chronos?) could comment…
There’s a lot more that we don’t know about black hole entropy than we do. But to summarize what we do know:
By a classical calculation, since black holes have “no hair”, they ought to have no entropy. This is definitely problematic, since objects with considerable entropy can turn into black holes.
It was noticed early on that certain aspects of black holes are closely analogous to thermodynamic properties. In particular, the total area of the event horizon(s) of a set of black holes never decreases. Thus, it is tempting to conclude that a black hole does, in fact, have an entropy, proportional to the area of its event horizon.
That still leaves the question of the proportionality factor. The obvious choice would be Planck units. And this is supported by Hawking radiation, which can be derived without recourse to thermodynamics, or can be derived entirely from thermodynamics assuming that proportionality, with the same results.
Certainly, the proportionality factor must be very, very large (i.e., a very high entropy per area), because anything at all can form a black hole, and the black hole, being the final state, must have at least as much entropy as its precursor (if the laws of thermodynamics are to hold).
But then there’s the question of how a “hairless” black hole can have any entropy at all, let alone such a high one. The usual answer nowadays is that the no-hair theorem is a purely classical result, and that in a proper quantum theory of gravity, a black hole would have some sort of microstructure in its event horizon that would contain all of the information. But unfortunately, we don’t have a quantum theory of gravity, so we can’t verify that. The String Model sort of predicts it, but then, the String Model can predict absolutely anything if you really set to it.
Personally, I suspect (though this doesn’t even really rise to the level of a hypothesis) that black holes have entropy of a different sort, that doesn’t require a microstate, similarly to how subatomic particles have angular momentum of a different sort, that doesn’t require rotational motion (but which is nonetheless interchangeable with the ordinary sort).
There’s a growing research program whose origin was the proposal that BH entropy can be explained as entanglement entropy across the horizon. In quantum field theory, vacuum states typically have a high degree of (‘short-range’) entanglement, so if you throw away (or hide behind a horizon) a portion of such a state, you’ll be left with something that has a high amount of (von Neumann) entropy, which in fact scales as the area of the ‘hole’.
This entanglement entropy is indeed not straightforwardly explained in terms of microstates of the system—if I take an entangled state, which has zero entropy (such as a Bell state), I can ‘forget’ about the entanglement and replace each local state with one that yields the same local measurement results, wich will invariably be a maximally mixed state (of maximum entropy). Only access to all parts of the system allows one to tell the difference, by investigating the correlations between the parts.
This is somewhat difficult to make precise—naively, the entanglement entropy of a qft vacuum state is divergent, and so far, there are only toy cases where we have an exact picture, such as the AdS/CFT correspondence. But there, we have some remarkable results, notably that the degree of entanglement between different parts of the CFT determines the connectedness of the AdS-spacetime—if you disentangle two boundary CFT regions, the bulk spacetime likewise partitions into two disconnected pieces.
This has motivated the proposal that spacetime, generally, is built from entanglement, making it an emergent phenomenon. This suggests that so is gravity, and indeed, there’s a famous argument (due to Ted Jacobson) according to which, in the presence of a horizon (i. e. an area law), Einstein’s equations can be obtained from thermodynamic considerations, as an equation of state for the spacetime. In this sense, trying to directly quantize gravity might be a bit of a red herring, since it’s ultimately just a macroscopic, emergent effect associated to the thermodynamics of entanglement (prompting Susskind to conjecture that we have some form of spacetime and gravity whenever we have quantum mechanics).
Of course, this is all highly speculative and incomplete, at present, but it’s already attracting enough hype that people claim to have created wormholes on their quantum computers . Still, though, I think it’s some of the most exciting research in recent years.