Say you put a computer into a box that can recycle the heat generated by the computer back into electricity (which goes back into powering the computer) with 100% efficiency (we’ll pretend the computer leaks energy only through heat.) You then start the computer on a task that will take a long time, like calculating the 1 billionth prime. Assuming it doesn’t break down can this computer run forever by recycling its energy output?
My feeling is no; the calculations are altering the entropy of the system which will eventually use up the energy contained in the system. If so, how much energy is this? What other possibilities are there?
Energy is not “used up”. If energy is not leaking from the system (since it recaptures the heat energy), then the energy of the system will remain constant.
In addition to all the above, I can conceive of no reason why the situation would be different if the computer were calculating the billionth prime vs. if the computer were just flipping one bit over and over. [Not doing much computing at all, just turning electricity into heat…]
That’s exactly my point. The computer is doing work (i.e. calculating primes) but a simplistic review of the system indicates it can run forever. So either:
Calculating primes is not considered work when applying the Second Law (and thus the computer runs forever).
or
It is work and something must be sapping the energy of the system until it fails. The only thing I can think of that could be an energy sink is the the decreasing information entropy of the data in the computer.
The fact that it’s calculating primes isn’t particularly significant. You could ask the same question if all the work it was doing was spinning a reel of tape, or flipping the same bit over and over, or whatever.
(Standard disclaimer: I don’t know what I’m talking about.)
The thing that will eventually cause the system to fail in the real world is that heat is not recycled as energy with 100% efficiency. Assuming some counterfactual world and then wondering how it fits in with this one really doesn’t make sense.
For the record, calculating primes (or flipping bits) on a modern computer is guaranteed to be work by some very nice theory that ties together information and heat.
You can’t recycle heat without a temperature difference.
Putting a refrigerator in the box doesn’t work because all those do is leach heat and spit it out elsewhere. Since your box is self-contained, the hot air can’t be expelled, leaving you with no net decrease of temperature. If you were to, for instance, freeze the box from the outside, then you’re adding energy to the box from the outside, so it’s not actually a closed system.
Couldn’t you dvide the box up into sections? Cold air goes in one side, hot air in another. Heck you wouldn’t even need an air conditioner. Just make the computer’s ventilation systems piped into one section.
Assuming this magic computer that can violate the 2nd law of thermodynamics needs air cooling that is. This setup makes about as much sense as plugging a power strip into it’s self for current I think.
This is to be the answer, within the context of your problem. This would be an increase in information, which is an ordering of energy, rather than an increase in energy per se. Increasing information in a closed system while everything else stays the same would be a decrease in entropy, in violation of thermodynamics, but that’s what you’re positing.
When you say “This would be an increase in information”, are you referring to some aspect of the problem which would not be there if the computer were merely flipping the same bit over and over?
The way I see it, you can actually look at this by ignoring what the computer is doing and treat it as if it were a simple electric-driven heat generator. In this case, if you have a heater driving a heat engine, powering a generator, driving the heater, will it run forever? The answer is no, of course, because the heat engine cannot even in an ideal case recapture all of the energy used to power the heater. Your heat engine requires a cold sink to operate. Heat flows through your heat engine from the hot to the cold sink, with some non-zero amount of energy going into heating the cold sink. Gradually the heat of the cold sink will increase, and the heat of the hot side will decrease, and the amount of available energy in the system will drop until you have an unpowered computer at room temperature.
Where on earth did I say I was adding energy from the outside? You mean the fans or whatever this supposed computer uses to keep from over heating? If so that’s an interesting assumption you made.
The assumption I made was what ever kept it from over heating (for example fans) would be part of the computer’s total load. Sort of like how a car’s radiator runs off energy produced from the engine and not a really long extension cord you drag down the highway.
Just flipping the same bit over and over won’t lead to an increase in information; you’re just revisiting the same state over and over. (I suppose real computers always have their memory in some state, and you’d need a quantum computer that could start with memory in a superposition of states to truly have in increase in information when calculating primes, but that’s just obscuring the issue.)
The important point is that having the information on primes (or any information) doesn’t require more energy than not.
Well, my point is, as far as I can tell, thermodynamically, the situation in the OP is not any different from that where a computer is just flipping the same bit over and over, or just directly converting electricity into heat, as AndrewL points out. The fact that it happens to be computing primes seems to me a red herring, and all the business about this being production of information and thus invoking entropy seems to me necessarily misguided and distracting.
He’s mixing up entropy and energy. I don’t see how describing a system with neither changing will help him distinguish between them. If we’re not doing any calculations, and nothing’s changing, why do we need a computer or even a heater? We could just put a warm rock in a box.