## Tuesday, July 31, 2018

### Sabine Hossenfelder clarifies entropy

1. Entropy doesn’t measure disorder, it measures likelihood.

Really the idea that entropy measures disorder is totally not helpful. Suppose I make a dough and I break an egg and dump it on the flour. I add sugar and butter and mix it until the dough is smooth. Which state is more orderly, the broken egg on flour with butter over it, or the final dough?

I’d go for the dough. But that’s the state with higher entropy. And if you opted for the egg on flour, how about oil and water? Is the entropy higher when they’re separated, or when you shake them vigorously so that they’re mixed? In this case the better sorted case has the higher entropy.

Entropy is defined as the number of “microstates” that give the same “macrostate”. Microstates contain all details about a system’s individual constituents. The macrostate on the other hand is characterized only by general information, like “separated in two layers” or “smooth on average”. There are a lot of states for the dough ingredients that will turn to dough when mixed, but very few states that will separate into eggs and flour when mixed. Hence, the dough has the higher entropy. Similar story for oil and water: Easy to unmix, hard to mix, hence the unmixed state has the higher entropy.