[oh_my_goodness]

>This is how I have come to understand entropy. The words disorder and order are a proxy for information content

Does information content mean this? ... "How many bits of random-number generator would I need to make the number of micro-states in the macro-state?"

[vishnugupta]

That is my mental model, yes. More bits are needed to capture more detailed (or micro-states as you called it elsewhere in this thread, or finer-grained) information.

Let's say there's a stone, we want to know its details. If all we want to know is whether it weighs more than 100KG or not then one bit will do. 1 means > 100KG and 0 means < 100KG. If we want to know its colour (as one of 7 WIBGYOR) as well then we need 4 bits; 3 bits to encode 7 colours and 1 bit to encode yes/no for the weight. And so on..as we gain more and more information we need more bits to store that.

This is just for the storage though; in order to gain the information we need to expend energy. More information requires more energy leading to more disorder as expending energy releases heat and thus 2nd order of thermodynamics as well as arrow of time. IMO our perception of time is purely based on memory which is information content of event stored in Neurons.

Quite a bit of hand-wavy. But this is a mental model I've developed over the years of thinking and reading (and listening to lectures) about entropy, information, arrow of time, and energy and how they are interconnected.

[lubesGordi]

The article does say that some crystalline structures can have more entropy (information) than their fluid state. How could that be? Any ideas on what that fluid state might be? The information content in a crystal is really low.

[vishnugupta]

Unfortunately the author doesn't explain it beyond sharing a reference to this paper[1] which is way beyond my competence.

[1] https://www.nature.com/articles/nature08641

[lubesGordi]

Beyond me too, but I'm going to assume that this is sort of an edge case where fluid crystalline structure can have less entropy than the static version (sort of sounds like the laminar flow state has less complex structure than its packed solid state). I doubt it contradicts your description above (which is similar to my understanding as well).