alt Hacker NewsGood question. You are absolutely right that entropy is always fundamentally a way to describe are our lack of perfect knowledge of the system [0].
Nevertheless there is a distinct "reality" to entropic forces, in the sense that it is something that can actually be measured in the lab. If you are not convinced then you can look at:
https://en.wikipedia.org/wiki/Entropic_force
and in particular the example that is always used in a first class on this topic:
https://en.wikipedia.org/wiki/Ideal_chain
So when viewed in this way entropy is not just a "made-up thing", but an effective way to describe observed phenomena. That makes it useful for effective but not fundamental laws of physics. And indeed the wiki page says that entropic forces are an "emergent phenomenon".
Therefore, any reasonable person believing in entropic gravity will automatically call gravity an emergent phenomenon. They must conclude that there is a new, fundamental theory of gravity to be found, and this theory will "restore" the probabilistic interpretation of entropy.
The reason entropic gravity is exciting and exotic is that many other searches for this fundamental theory start with a (more or less) direct quantization of gravity, much like one can quantize classical mechanics to arrive at quantum mechanics. Entropic gravity posits that this is the wrong approach, in the same way that one does not try to directly quantize the ideal gas law.
[0] Let me stress this: there is no entropy without probability distributions, even in physics. Anyone claiming otherwise is stuck in the nineteenth century, perhaps because they learned only thermodynamics but not statistical mechanics.
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> You are absolutely right that entropy is always fundamentally a way to describe are our lack of perfect knowledge of the system [0].
> [0] Let me stress this: there is no entropy without probability distributions, even in physics.
The second item doesn't entail the first. Probabilities can be seen as a measure of lack of knowledge about a system, but it isn't necessarily so. A phenomenon can also be inherently/fundamentally probabilistic. For example, wave function collapse is, to the best of our knowledge, an inherently non-deterministic process. This is very relevant to questions about the nature of entropy - especially since we have yet to determine if it's even possible for a large system to be in a non-collapsed state.
If it turns out that there is some fundamental process that causes wave function collapse even in perfectly isolated quantum systems, then it would be quite likely that entropy is related to such a process, and that it may be more than a measure of our lack of knowledge about the internal state of a system, and instead a measurement of the objective "definiteness" of that state.
I am aware that objective collapse theories are both unpopular and have some significant hurdles to overcome - but I also think that from a practical perspective, the gap between the largest systems we have been able to observe in pure states versus the smallest systems we could consider measurement devices is still gigantic and leaves us quite a lot of room for speculation.
Sure, I'm not denying that entropy exists as a concept, that can be used to explain things macroscopically. But like you said, it's origins are statistical. To me, temperature is also a similar "made up" concept. We can only talk about temperature, because a sufficiently large group of particles will converge to a single-parameter distribution with their velocities. A single particle in isolation doesn't have a temperature.
So if they say gravity might be an entropic effect, does that mean that they assume there's something more fundamental "underneath" spacetime that - in the statistical limit - produces the emergent phenomenon of gravity? So it isn't the entropy of matter that they talk about, but the entropy of something else, like the grains of spacetime of whatever.