Entropy at Play

While out and about this rainy Saturday I thought I’d buy a set of dominoes with which to play with my young visitor. During such play, since he started to count the numbers of dots on them spontaneously, and since as we unpacked them he exclaimed “zero!” excitedly at the one with no dots on (I found this impressive), I figured I’d encourage him to place them in order. This went along fine until he discovered that he was finding numbers he’d found before. I encouraged him to lay them next to each other when they match (this shows what we’d call “degeneracy” in my area), and carry on. Eventually, he found the nice shape in the picture. I decided it was a bit early to explain to a four year old that he’d just illustrated beautifully the fundamental understanding of the important concept “entropy”. Instead I mused to myself (as I often do when I talk about it in terms of rolling six sided dice in my physics 151 class) that if only more textbook (and other) presentations would focus on this simple type of example to talk about entropy*, instead of mumbling silly confusing and mostly irrelevant things about disorder, people would be less apt to switch off when the idea comes up.

-cvj

*Oh, you want an explanation? 😀 Ok, a quick start to get you going if unfamiliar… In thermodynamics, there are macroscopic things we measure for, say, a gas – like temperature, volume, pressure, etc.. That is like the total number of dots on a domino. But there are also microscopic details of the arrangements of the gas molecules. Sometimes there are many different microscopic arrangements that correspond to the same macroscopic state. The entropy is simply a measure of the degree of that multiplicity or “degeneracy”. So it is with the dominoes. There are many ways of arranging the dots to make some totals (like six, for example, that has the most ways – there are four dominoes that total six). Those totals have higher entropy than those with fewer ways, like zero or twelve. The same sort of reasoning can get you in a few more sentences to the understanding of why heat tends to spontaneously flow from high temperature to low temperature, giving you the second law of thermodynamics. Look it up. Notice: – Not a scrap of disorder enters this discussion of entropy. Hurrah!