Would Maxwell's demon having infinite memory storage break the second law of thermodynamics?

Question

Apologies if my understanding is wrong, I am literally a child.

Maxwell's demon is meant to break the second law of thermodynamics by making a disorderly system orderly (see image below).

But the issue is is that the demon has a finite memory and will have to erase it at some point. Landauer's principle asserts that erasing information from a physical system will always require performing work, and particularly will require at least $k_BT\ln(2)$ of energy to be spent and eventually released as heat.

So what if the demon had an infinite memory (think very powerful computers)? Would we see negentropy and an organised system?

Answer 1

But the issue is is that the demon has a finite memory and will have to erase it at some point. Landauer's principle asserts that erasing information from a physical system will always require performing work, and particularly will require at least kBTln(2) of energy to be spent and eventually released as heat.

So what if the demon had an infinite memory (think very powerful computers)? >Would we see negentropy and an organised system?

The entropy of the gas would decrease and the entropy of the memory would increase.

Alternatively we could say that the information in the gas would decrease and the information in the memory would increase.

A similar arrangement that occurred to me is a Maxwell's demon with large thermal mass at absolute zero temperature. Now erasing bits from demon's memory would require zero energy according to $E=k_BT\ln(2)$. The point here is that zeroed out memory and thermal mass at absolute zero are kind of similar things.

Here is a more complete example about the aforementioned similarity between zeroed memory and matter at absolute zero temperature:

With large amount of zeroed memory a Maxwell's demon can power a cart driving around in a closed hall, using the thermal energy of the air in the hall, which air is cooled by the demon and heated by the turbulence at the car's wake. This sounds quite a lot like breaking of the second law of thermodynamics, but actually that law is not broken, as the entropy of the memory is increasing, while the temperature and energy of the memory are not increasing at all, because the demon converts the heat energy to mechanical energy at 100% efficiency.

With a small amount of matter at absolute zero temperature being used as a heat sink, a heat engine can power a cart driving around in a closed hall, using the thermal energy of the air in the hall, which air is cooled by the engine and heated by the turbulence at the car's wake. This sounds quite a lot like breaking of the second law of thermodynamics, but actually that law is not broken, as the entropy of the mass at absolute zero is increasing, while the temperature and energy of the matter at absolute zero are not increasing at all, because the engine converts the heat energy to mechanical energy at 100% efficiency.

Answer 2

Yes. You self answered your question. If such an infinite demon exist then it would break the second law of thermodynamics. If not, then it will not break it.