Entropy is a word that gets thrown around quite a bit. Often times “disorder” is used as a synonym for entropy. This works pretty well most of the time. For example, scrambled egg has higher entropy than an uncooked one and a paper-strewn desk has higher entropy than a tidy one. But there are some instances where making the disorder-entropy equivalence can get us into trouble.
For example, imagine a glass filled with crushed ice and water. Imagine an identical glass filled with just water. Which has higher entropy? Which is more “disordered”? Most people I know would say the glass with the crushed ice looks more disorderly, but it is the glass with just water that has higher entropy. Why?
Entropy is really a measure of how many ways you can rearrange something and have it look the same. The number of ways you can rearrange the water molecules in a glass of liquid water is smaller than the number of ways you can rearrange the glass with the ice.