[jbay808]

No, it is subjective. We just only have such blunt instruments for practically measuring states, relative to the gargantuan amount of entropy in most real systems, that the subjective nature of entropy is easy to miss. But in a world where the frontiers of thermodynamics have moved from steam engines to lasers, computers, DNA, and black holes, the difference is increasingly obvious and important.

With steam engines, we got away with treating a volume of gas as having not only a few parameters that we knew and cared about, like mass, temperature and pressure, but we could further deceive ourselves into thinking that those were the only parameters that existed to describe the system. The only parameters that were knowable. But Boltzmann knew better.

Look at Boltzmann's formula, S = kB log W.

For any single particular system you describe to me, W will be 1, and so S will be 0. So it's only if you describe an ensemble of systems -- that is, if you describe a system vaguely, such that I am left to imagine the details -- that we have nonzero entropy. If you ask me to calculate the entropy of that "system", that macrostate, that ensemble, then sure, I'll end up with nonzero entropy. But if I ask you to keep transmitting more data about the scenario, then with each further description, you'll be narrowing the state space and thereby decreasing the entropy.

Look, since the entropy of a macrostate is nonzero, but the entropy of any single microstate which is consistent with that macrostate is zero, it's clear that entropy is not an intrinsic property of any real system. It's a property of how many other possible non-existent systems could be swapped out for the one in front of you, without you noticing the change.

If I swap out the air in your room for an equal volume of air at equal temperature and pressure, you probably won't notice.

If I swap out the hard drive in your laptop for an equal volume of hard drive at equal temperature and pressure, you probably will!

[raattgift]

Maybe better to say that the universe does not appear to pick out a single coarse-graining or fine-graining procedure for practically any system.

For instance, following your Boltzmannian example, I think one would notice swapping 1 µm³ of the r/w head and 1 µm³ of the recording surface of a new, freshly powered on HDD more than one would notice substituting the entire HDD for a new one of the same model and turning that on. And here I am already using units of length (cf. "equal volume"), and we know neither units nor lengths are generally picked out by the universe.

[deltaonefour]

Very few people know this but.

Information entropy and statistical mechanical entropy are two different things.

They share the same equation and the same name but they are two unrelated concepts. You have conflated the two. The person you are responding to is referring to statistical entropy.

Basically in this entire thread nobody, including you, is fully grasping the situation.

[chermi]

They are not at all unrelated. It is not easy to grasp, so I understand the confusion. https://en.m.wikipedia.org/wiki/Landauer%27s_principle

Fun rabbit hole would start with classic paper by jaynes

Many more recent examples relating bit erasure costs of computation. Some names to look up if interested include charlie Bennet,Dave wolpert, James crutchfield, Susanne still, for starters.

Edit -- a collection of ideas related to this problem and mixing in "complexity" can be found in SFI proceedings called "Complexity, entropy, and the physics of information"

[jbay808]

I respectfully disagree. Perhaps you'd like to present more than a mere assertion to make your case. I did.

If it helps, here's a paper that explains my stance in more detail. https://bayes.wustl.edu/etj/articles/theory.1.pdf

[kgwgk]

If you think there is no relation between the different things called entropy apart from the name maybe you're not fully grasping the situation either.