or erase them (which just moves them to the environment)
I don’t follow this. In what sense is a bit getting moved to the environment?
I previously read deconfusing Landauer’s principle here and… well, I don’t remember it in any depth. But if I consider the model shown in figures 2-4, I get something like: “we can consider three possibilities for each bit of the grid. Either the potential barrier is up, and if we perform some measurement we’ll reliably get a result we interpret as 1. Or it’s up, and 0. Or the potential barrier is down (I’m not sure if this would be a stable state for it), and if we perform that measurement we could get either result.”
But then if we lower the barrier, tilt, and raise the barrier again, we’ve put a bit into the grid but it doesn’t seem to me that we’ve moved the previous bit into the environment.
I think the answer might be “we’ve moved a bit into the environment, in the sense that the entropy of the environment must have increased”? But that needs Landauer’s principle to see it, and I take the example as being “here’s an intuitive illustration of Landauer’s principle”, in which case it doesn’t seem to work for that. But perhaps I’m misunderstanding something?
(Aside, I said in the comments of the other thread something along the lines of, it seems clearer to me to think of Landauer’s principle as about the energy cost of setting bits than the energy cost of erasing them. Does that seem right to you?)
I think the answer might be “we’ve moved a bit into the environment, in the sense that the entropy of the environment must have increased”?
Yes, entropy/information is conserved, so you can’t truly erase bits. Erasure just moves them across the boundary separating the computer and the environment. This typically manifests as heat.
Landauer’s principle is actually about the minimum amount of energy required to represent or maintain a bit reliably in the presence of thermal noise. Erasure/copying then results in equivalent heat energy release.
I don’t follow this. In what sense is a bit getting moved to the environment?
I previously read deconfusing Landauer’s principle here and… well, I don’t remember it in any depth. But if I consider the model shown in figures 2-4, I get something like: “we can consider three possibilities for each bit of the grid. Either the potential barrier is up, and if we perform some measurement we’ll reliably get a result we interpret as 1. Or it’s up, and 0. Or the potential barrier is down (I’m not sure if this would be a stable state for it), and if we perform that measurement we could get either result.”
But then if we lower the barrier, tilt, and raise the barrier again, we’ve put a bit into the grid but it doesn’t seem to me that we’ve moved the previous bit into the environment.
I think the answer might be “we’ve moved a bit into the environment, in the sense that the entropy of the environment must have increased”? But that needs Landauer’s principle to see it, and I take the example as being “here’s an intuitive illustration of Landauer’s principle”, in which case it doesn’t seem to work for that. But perhaps I’m misunderstanding something?
(Aside, I said in the comments of the other thread something along the lines of, it seems clearer to me to think of Landauer’s principle as about the energy cost of setting bits than the energy cost of erasing them. Does that seem right to you?)
Yes, entropy/information is conserved, so you can’t truly erase bits. Erasure just moves them across the boundary separating the computer and the environment. This typically manifests as heat.
Landauer’s principle is actually about the minimum amount of energy required to represent or maintain a bit reliably in the presence of thermal noise. Erasure/copying then results in equivalent heat energy release.