# Question on “The more information you have about a system, the more work you can extract from it”

This was said in the comments (#15/#27) of this Scott Aaronson post about "information is physical" and reaffirmed by Sean Carroll and praised by Scott among others.

https://www.scottaaronson.com/blog/?p=3327

Could someone explain the case when the information about a system is seemingly human specific/abstract? I am having trouble imagining how labeling particles with letters in a Laplace's demon type setup mechanically allows for more work to be extracted. Letter designation a form of information right? I believe I've read that recording information doesn't necessarily have a lower energy bound requirement, only erasing/changing information does? Are these two statements (title and previous sentence) somehow equivalent?

For that matter, if I just put a letter A on a piece of paper I can do more work?

Information is not simply human-specific. Just ask your computer, which stores tons of information :)

The "you" here can be any information storage-and-retrieval system; there is nothing about theory that obligates it be a human being, or even that it code its information in any form recognizable to humans.

Maxwell's demon can help one in understanding the principle. For those who don't know, this is a thought experiment in which a tiny "demon" is imagined to watch over the molecules in a hot gas in a chamber, initially at thermal equilibrium, and has a door it can open/close to let molecules into another, initially empty, chamber, so that it can, say, let only fast molecules through, thus causing an accumulation of fast molecules in the other, empty, chamber, while the initial chamber becomes dominated by slow molecules. The once-equilibrium gas has now been partitioned into two reservoirs at different temperatures.

Now for the article. The problem is that, in the usual setup, this requires some form of sensing capacity on the demon, which, thanks to a famous argument, must then dissipate energy, and so it cannot be used to extract any work.

But suppose that instead, the demon were loaded up with exact information about the movements of all the molecules in the system in advance (We will ignore quantum mechanics for now, as thermodynamics applies both classically and quantumly). Then, by definition, it can extrapolate their movements using the laws of dynamics so as to know exactly when to open and close its gate to let the fast molecules through without any sensing, thus achieving the same sortition. You can now run a heat engine between the two, and there's your work output.

• But still how would someone labeling 1 particle in box of particles then allow them to do more work. I am not doubting the arguments. I or the demon can label 1 of the particles in our head costing no energy, or do it ahead of time like in your last paragraph. Now I know more information about the particle system than the setup without any extra labels. How then do I extract more work? Is it because I am part of the system with the label in my head and some external system could then use me in some way? How would they use me. – J Kusin Sep 14 at 15:15
• No, merely putting a label on them doesn't do it. The trick is not you having information, or the system having information, alone, it's the gap between how much you have and how much you could have. The smaller that gap, the more work you can do. – The_Sympathizer Sep 15 at 1:54
• Putting a label increase how much information you do have - but more subtly, it at the very least does not shrink that gap, because it introduces some extra freedom in the system: namely, to which particle the label is attached. If you only know that one particle is labeled, but not which, the gap is actually larger by $\lg(N)$, where $N$ is the number of particles in the system, so in fact, you can actually do less work, not more. And if you do know which, you gain precisely nothing: the gap is unchanged. And those, of course, are just the second law in action. – The_Sympathizer Sep 15 at 1:58
• Thank you, I will have to think about this some more to really get it but you drove it home for me. And when comparing two different observers of a system, you could or would compare the gaps of their individual "known vs could know"'s , and two observers could extract two different amounts of work from the same system? And at least in terms of SM, we've all agreed on a shared way to coarse-grain for (all?) systems? – J Kusin Sep 15 at 2:07