> The state of each card. If you define a macrostate in such a way as it can have only one microstate, then yes, entropy is 0. It is also completely artificial.

> The state of each card. If you define a macrostate in such a way as it can have only one microstate, then yes, entropy is 0. It is also completely artificial. Obviously, a deck of cards can be in a lot of different microstates, I'm not sure what do you mean ? Consider that "macrostate" is another name for "distribution" ? > There is indeed some overlap (I have personally worked for a couple of years on applying information theory to calculate entropy in glass-forming materials), but not enough that you can just apply random concepts from one field to the other. Basically, your interpretation is that "we know a lot about the system, therefore entropy is low", whilst in a physical system it's the other way around: "entropy is low, therefore we know a lot about it". Knowing something does not change the state of the system you are observing. This is why having two different terms "entropy" and "lack of information" that correspond to the same underlying physical concept is problematic : it causes this kind of confusion. Knowing a lot about a system is equivalent to having low entropy about it. > Entropy itself is whatever it is even before we bother calculating it, and we can estimate it different ways. [...] Entropy is a thermodynamical property of a bit of stuff, regardless of what we know about it. The conservation of Gibbs free energy does not suddenly break down because we stop (or start) looking. "Looking" (aka "measurement" or "observation") is not a "free" operation. To go back to the example of the deck of cards, the deck would have needed to be prepared beforehand to be "ordered", and the action of "looking" at it and to check in what order each card is in is not "free" either. In the same way, neither constructing an aligned spin system nor checking its alignment are "free". As another example, consider the Szilard engine, which allows us to "extract" energy "from" information : https://www.pnas.org/content/111/38/13786 https://www.pnas.org/content/111/38/13786 (Semi-)Classical entropy is defined in terms of probability, it's a functional that depends on a specific probability distribution (aka macrostate) : it's the expected value (aka weighted average) over the surprisals (aka information contents) of all the possible outcomes (aka microstates). (There's also a generalization of it for the situations where we have entangled microstates and quantum mechanics really come into play.) As far as we know, this model works for all the situations where the two nuclear forces and/or relativistic effects can be neglected.