Comment by simiones

> 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.