I think this comment is based on a misunderstanding of what an insulator is. Heat isn’t a particle that you need to throw up an energy barrier to block. Heat is energy, or more specifically, energy that carries information (in particular random information, aka thermal noise). How well insulated two systems are is a function of how they interact. A good way of thinking of it is that the systems both have a lot of internal degrees of freedom, plus each has some “edge” degrees of freedom. The systems interact with each other through their edge degrees of freedom, and the exact nature of this interaction determines how fast heat can flow between them. A stronger interaction typically translates to a faster rate of heat flow.
(Ironically, if we write down the interaction using a Hamiltonian, scaling up the Hamiltonian both increases the ΔE between its eigenvalues, and makes the interaction stronger (i.e. increases the rate of heat flow). So higher ΔE translates to having a worse insulator.)
What I mean is that “the bit is in the radiator” is another state of the system where a two-level subsystem corresponding to the bit is coupled to a high-temperature bath. There’s some transition rate between it and “the bit is in the CPU” determined by the radiator temperature and energy barrier between states. In particular, you need the same kind of energy “wall” as between computational states, except that it needs to be made large compared to the bath temperature to avoid randomly flipping your computational bit and requiring your active cooling to remove more energy.
This seems to be more or less the same thing that jacob_cannell is saying in different words, if that helps. From your responses it seems your internal picture is not commensurate with ours in a number of places, but clarifying this one way or the other would be a step in the right direction.
Okay, thanks for clarifying. Treating “the bit is in the radiator” as a state of the system still seems a little like a strange way of phrasing it under my model. I would say something like “we have a particle in the CPU and a particle in the Radiator, each of which has 2 states so it can represent a bit. So the combined system has the states being: 00, 01, 10, 11. Moving the bit between the CPU and the Radiator looks like performing the following reversible mapping: 00 → 00, 01 → 10, 10 → 01, 11 → 11. (i.e. the bits are just swapped). The CPU and Radiator need to be coupled to achieve this mapping. Now to actually have moved a bit from the CPU to the radiator, rather than just have swapped two bits, something needs to be true about the probability distribution over states. In particular, we need the bit in the radiator to be 0 with near certainty. (i.e. P(01) and P(11) are approximately 0) This is the entire reason why the Radiator needs to have a mechanism to erase bits, so it can have a particle that’s almost certainly in state 0 and then that negentropy can be sent back to the CPU for use in computations.
So it sounds like you’re concerned with the question of “after we erase a bit, how do we keep it from being corrupted by thermal noise before it’s sent back to the CPU?” The categories of solution to this would be:
Keep it well isolated enough and send it back quick enough after the erasure is completed that there’s no opportunity for it to be corrupted.
Stick up a high energy wall between the states so the bit can persist for a long time.
Either one of these would be fine from my perspective, I guess you and Jacob would say that we have to go with 2, and if you have that assumption then even the simple straightforward argument depends on being able to manipulate the energy wall without cost. I do think you can manipulate energy walls without cost, though. See my discussion with Jacob, etc.
I think this comment is based on a misunderstanding of what an insulator is. Heat isn’t a particle that you need to throw up an energy barrier to block. Heat is energy, or more specifically, energy that carries information (in particular random information, aka thermal noise). How well insulated two systems are is a function of how they interact. A good way of thinking of it is that the systems both have a lot of internal degrees of freedom, plus each has some “edge” degrees of freedom. The systems interact with each other through their edge degrees of freedom, and the exact nature of this interaction determines how fast heat can flow between them. A stronger interaction typically translates to a faster rate of heat flow.
(Ironically, if we write down the interaction using a Hamiltonian, scaling up the Hamiltonian both increases the ΔE between its eigenvalues, and makes the interaction stronger (i.e. increases the rate of heat flow). So higher ΔE translates to having a worse insulator.)
What I mean is that “the bit is in the radiator” is another state of the system where a two-level subsystem corresponding to the bit is coupled to a high-temperature bath. There’s some transition rate between it and “the bit is in the CPU” determined by the radiator temperature and energy barrier between states. In particular, you need the same kind of energy “wall” as between computational states, except that it needs to be made large compared to the bath temperature to avoid randomly flipping your computational bit and requiring your active cooling to remove more energy.
This seems to be more or less the same thing that jacob_cannell is saying in different words, if that helps. From your responses it seems your internal picture is not commensurate with ours in a number of places, but clarifying this one way or the other would be a step in the right direction.
Okay, thanks for clarifying. Treating “the bit is in the radiator” as a state of the system still seems a little like a strange way of phrasing it under my model. I would say something like “we have a particle in the CPU and a particle in the Radiator, each of which has 2 states so it can represent a bit. So the combined system has the states being: 00, 01, 10, 11. Moving the bit between the CPU and the Radiator looks like performing the following reversible mapping: 00 → 00, 01 → 10, 10 → 01, 11 → 11. (i.e. the bits are just swapped). The CPU and Radiator need to be coupled to achieve this mapping. Now to actually have moved a bit from the CPU to the radiator, rather than just have swapped two bits, something needs to be true about the probability distribution over states. In particular, we need the bit in the radiator to be 0 with near certainty. (i.e. P(01) and P(11) are approximately 0) This is the entire reason why the Radiator needs to have a mechanism to erase bits, so it can have a particle that’s almost certainly in state 0 and then that negentropy can be sent back to the CPU for use in computations.
So it sounds like you’re concerned with the question of “after we erase a bit, how do we keep it from being corrupted by thermal noise before it’s sent back to the CPU?” The categories of solution to this would be:
Keep it well isolated enough and send it back quick enough after the erasure is completed that there’s no opportunity for it to be corrupted.
Stick up a high energy wall between the states so the bit can persist for a long time.
Either one of these would be fine from my perspective, I guess you and Jacob would say that we have to go with 2, and if you have that assumption then even the simple straightforward argument depends on being able to manipulate the energy wall without cost. I do think you can manipulate energy walls without cost, though. See my discussion with Jacob, etc.