That was a simplified account of what is going on. To include the full system, you would have to include the means by which the Demon recorded the knowledge. However it’s recorded, it overwrites the information that was otherwise contained in that recording mechanism (i.e., mutual information with some environment), and this deletion of mutual information is an increase in entropy.
But in such an accounting, you would have three systems, which complicates the scenario. In the example given, the Demon is implicitly taken to include the Demon’s recording devices (even if that’s his brain). The fact that it has destroyed some relationship between some system (the recording device) and another is represented as higher Demon entropy that retains independence from the Y system. (There are extra states the Demon can have that have nothing to do with Y.)
I guess it would seem to me that what gets “overwritten” is the (now invalid) knowledge of where Y is, and what it is overwritten with is the new, valid position of it. I’ll have to chew on it for a while.
By the way, sort of unrelated, but I’ve always wondered why gravity acting on things is not considered a loss of entropy. For example I can drop a bowling ball from multiple distances, but it will always end up 0 feet from the ground:
B4 → B0
B3 → B0
B2 → B0
etc.
The only thing I can think of is that, when the ball hits the ground the collision creates enough heat (i.e. entropy) to balance everything out. Is that correct?
Yes, that’s basically correct: the ball ends up at the same place, but differs in another state—velocity—which gives a different result for how much momentum it imparts to the earth, or heat energy it generates through friction, or elastic energy in compressing its foundation.
Btw, note that there is a connection between the energy of a system and the information it stores. Higher energy states are less likely and therefore store more information. (See Academician’s recent post on informativeness in information theory.) Because energy of a state is relative to another, this suggests a research program that breaks down the laws of physics into rules about changes in informational content. I’m still in the process of finding out how much work has been done on this and what’s left to do.
That was a simplified account of what is going on. To include the full system, you would have to include the means by which the Demon recorded the knowledge. However it’s recorded, it overwrites the information that was otherwise contained in that recording mechanism (i.e., mutual information with some environment), and this deletion of mutual information is an increase in entropy.
But in such an accounting, you would have three systems, which complicates the scenario. In the example given, the Demon is implicitly taken to include the Demon’s recording devices (even if that’s his brain). The fact that it has destroyed some relationship between some system (the recording device) and another is represented as higher Demon entropy that retains independence from the Y system. (There are extra states the Demon can have that have nothing to do with Y.)
Did that make any sense?
I guess it would seem to me that what gets “overwritten” is the (now invalid) knowledge of where Y is, and what it is overwritten with is the new, valid position of it. I’ll have to chew on it for a while.
By the way, sort of unrelated, but I’ve always wondered why gravity acting on things is not considered a loss of entropy. For example I can drop a bowling ball from multiple distances, but it will always end up 0 feet from the ground:
B4 → B0
B3 → B0
B2 → B0
etc.
The only thing I can think of is that, when the ball hits the ground the collision creates enough heat (i.e. entropy) to balance everything out. Is that correct?
Yes, that’s basically correct: the ball ends up at the same place, but differs in another state—velocity—which gives a different result for how much momentum it imparts to the earth, or heat energy it generates through friction, or elastic energy in compressing its foundation.
Btw, note that there is a connection between the energy of a system and the information it stores. Higher energy states are less likely and therefore store more information. (See Academician’s recent post on informativeness in information theory.) Because energy of a state is relative to another, this suggests a research program that breaks down the laws of physics into rules about changes in informational content. I’m still in the process of finding out how much work has been done on this and what’s left to do.