# Residual Entropy 1/26/21

Science with Richard Bleil

Today a meme came to my attention likening betrayal of faith to a crumpled piece of paper. It suggested that once you’ve broken that faith in a relationship, even when you try to smooth out the relationship again, those ripples remain, much like the wrinkles in a piece of paper that has been crumpled and smoothed back out.

In thermodynamics, we refer to this as “residual entropy”. Entropy, many people know, is often thought of tending towards a state of disorder. I’ve discussed how this is a poor definition of entropy in a previous post, but for this one it’s a sufficient way to think of it. The second law of thermodynamics suggests that natural processes tend towards increased entropy or disorder. We see examples of this every day; our houses tend to decay if we don’t keep up with maintenance, the roads tend to decay requiring regular construction and repair, heck, even our lives tend to chaos. At least I know mine does unless I put in the work to keep it in check.

The second law is frequently misquoted, with many people believing that it says that entropy can never decrease. This is not true. The entropy of a system can decrease by doing work on the system. The entropy of the universe, however, can never decrease. This means as we decrease the entropy of a system, the entropy of the system’s surroundings must increase at least as much as the entropy of the system decreases, and usually more. When we say “work on the system”, what we mean is that we need to expend energy to decrease the entropy of the system. Work is defined as force (like the force of gravity) times distance. As an example, I just alphabetized my DVD collection (yes, I still own DVD’s). I decreased the entropy of the collection as now it is easier to find specific movies, and I did it by physically moving the DVD’s around. I did work on the system, and the entropy decreased.

“Residual entropy” is the concept that even as we reduce the entropy of a system, there is always some entropy left over that we can never completely dispense. One example is wrinkles in a piece of paper once it’s been crumpled. If a paperclip bends out of shape, it’s impossible to ever completely get the paperclip back to its original form. There’s just always some disorder there.

You might be wondering where the residual entropy might be in my movie collection. Well, first of all, there is the possibility that some of them are out of order, but frankly, that’s kind of a trivial answer. No, residual entropy here is probably the entropy of the surroundings as a result of the work I did. As I moved the DVD’s, I used energy. This burned sugar, my body’s source of energy, converting it to carbon dioxide and thus creating entropy in the surroundings. It’s not obvious in this case, but there will always be residual entropy in anything that we do.

We see residual entropy in roads after it’s been repaired; that uneven bump where a patch was put down, or where the new stretch of road connects to the original. This is all residual entropy.

In a relationship, once someone has had an affair, this increases the entropy of the relationship. Entropy is uncertainty, and if a spouse has an extramarital affair, there is uncertainty in the mind of the other party. Can this entropy ever be reduced? Well, maybe, but you have to put work into the relationship to try to bring this uncertainty back down, perhaps through marriage counseling, and maybe with time. The problem is no matter how much work goes into repairing the relationship, and no matter much time passes, there will always be that seed of doubt planted in the mind that it happened once, why couldn’t it happen again? That’s a form of residual entropy.

It never ceases to amaze me just how a knowledge of thermodynamics and chemistry can influence the way you view the world. I recently had a conversation and argued that everything, including abstract ideas, must follow the laws of thermodynamics. It felt as if the conversation was about to become far more intense than was worth so I let it go. Nonetheless, even in this blog, a very real concept in thermodynamics naturally led us to a very human (and painful) piece of our everyday life, and something that’s far too common for us as well. Still, I’ll again be looking around for further examples of residual entropy for quite some time.