Excuse me, the thought somehow rotated 180 degrees between brain and fingers. My point from a couple of exchanges up remains: How did you come to know this quantum state? If you magically inject information into the problem you can do anything you like.
Well no, it’s not impossible, but the chance of it happening is obviously 2^-N, where N is the number of bits required to specify the state. It follows that if you have 2^N states, you will get lucky and extract useful work once; which is, of course, the same amount of useful work you would get from 2^N states anyway, whether you’d made a guess or not. Even on the ignorance model of entropy, you cannot extract anything useful from randomness!
Measurements work well if you want to know what quantum state something is in. Or alternately, you could prepare the state from scratch—we can do it with quite a few atoms now.
And I hardly think doing a measurement with low degeneracy lets you do anything. You can’t violate conservation of energy, or conservation of momentum, or conservation of angular momentum, or CPT symmetry. It’s only thermodynamics that stops necessarily applying.
Measurements work well if you want to know what quantum state something is in. Or alternately, you could prepare the state from scratch—we can do it with quite a few atoms now.
Yes, ok, but what about the state of the people doing the measurements or the preparation? You can’t have perfect information about them as well, that’s second thermo for you. You could just as well skip the step that mentions information and say that “If we had a state of zero entropy we could make it do a lot of work”. So you could, and the statement “If we had a state that we knew everything about we could make it do a lot of work” is equivalent, but I don’t see where one is more fundamental, useful, intuitive, or correct than the other. The magic insertion of information is no more helpful than a magic reduction of entropy.
Excuse me, the thought somehow rotated 180 degrees between brain and fingers. My point from a couple of exchanges up remains: How did you come to know this quantum state? If you magically inject information into the problem you can do anything you like.
We guessed and got really lucky?
In other words, magic. As I said, if you’re allowed to use magic you can reduce the entropy as much as you like.
So is it impossible to guess and be lucky? Usually in this context the word “magic” would imply impossibility.
Well no, it’s not impossible, but the chance of it happening is obviously 2^-N, where N is the number of bits required to specify the state. It follows that if you have 2^N states, you will get lucky and extract useful work once; which is, of course, the same amount of useful work you would get from 2^N states anyway, whether you’d made a guess or not. Even on the ignorance model of entropy, you cannot extract anything useful from randomness!
Measurements work well if you want to know what quantum state something is in. Or alternately, you could prepare the state from scratch—we can do it with quite a few atoms now.
And I hardly think doing a measurement with low degeneracy lets you do anything. You can’t violate conservation of energy, or conservation of momentum, or conservation of angular momentum, or CPT symmetry. It’s only thermodynamics that stops necessarily applying.
Yes, ok, but what about the state of the people doing the measurements or the preparation? You can’t have perfect information about them as well, that’s second thermo for you. You could just as well skip the step that mentions information and say that “If we had a state of zero entropy we could make it do a lot of work”. So you could, and the statement “If we had a state that we knew everything about we could make it do a lot of work” is equivalent, but I don’t see where one is more fundamental, useful, intuitive, or correct than the other. The magic insertion of information is no more helpful than a magic reduction of entropy.