They are related by the Boltzmann equation. The intuitive interpretation is this: entropy is the amount of information required to determine a particular microstate from the associated macrostate. (This is how you solve Maxwell's demon)
(Note that I don't really know what I'm talking about, I'm just parroting what I remember from my information theory course)
I thought it was related to the number of micro states that are equivalent to a given macro state. So, as the number of particles increase, the temperature increases or the volume increases, there are more possible micro states. That’s why very cold things or very ordered things (crystals) have low entropy, because you can’t readily swap out microstates.
It’s also why a pile of legos is high entropy; you could easily swap legos around and the pile would be indistinguishable. Whereas you can’t do that with a built lego.
It's correct, but that point of view is not in contradiction with what I said.
You may imagine a macrostate as a state representing incomplete information. In order to uniquely determine the microstate, you need additional information proportional to the logarithm of the number of possible microstates.
Yes, that’s while I don’t frame as disorder but rather explain order in terms of the micro state-macro state relation. While a built lego set and a crystal are well ordered and have low entropy, order and entropy aren’t the same thing.
(Note that I don't really know what I'm talking about, I'm just parroting what I remember from my information theory course)