[galimaufry]

I'm not sure this answers the question. The wikipedia page is about the entropy of a probability distribution. But the information speed limit is supposed to apply even if everything is totally deterministic.

If I write a single, 100% certain message and put it in a spaceship it still cannot go faster than light, even though there is no information transfer (entropy of my message (a constant random variable) is 0).

(I'm not saying you are wrong, I am asking to be corrected)

[aeternum]

The spaceship itself represents a huge chunk of information (such as the atomic arrangement of the metal atoms making up the bolts).

[galimaufry]

I agree that there is "information" in the colloquial sense there, or even in the Kolmogorov sense. I don't understand how there is information in the entropy sense, because I do not see a random variable anywhere in this story.

[mannykannot]

I believe we are talking about Shannon's direct analogy between information and entropy here. The low probabliity of the atoms of the spaceship being arranged as they are - a specific design of a spaceship - out of all their possible arrangements, is a state of low entropy and high information content.

https://en.wikipedia.org/wiki/Entropy_(information_theory)

[jakeva]

That was what I was talking about, yes.

[aeternum]

Entropy isn't necessarily random. I think a better description of entropy might be unimportant states. For the rocket, we might care about the total mass and we might even care about the temperature of those bolts. Those parameters represent information.

But there's even more information in the rocket, specifically the momentum*position of each of the atoms within the bolt. That quantity for each atom is measurable/knowable and represents information.