Maxwell's Demon: Can Entropy Be Reversed?

Maxwell's Demon. Maxwell's famous thought experiment. Can we break the second law of thermodynamics? Can entropy be reversed?

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Today we are going to try to break the second law of thermodynamics! Remember that law? It comes in many forms:
1. The entropy/disorder of the universe is always increasing. But it can also be written as
2. The energy in the universe available to do useful work is always decreasing.

When things are in a low entropy ordered state, they can do what scientists call "useful work". Imagine a box with hot air on one side and cold air on the other. This is a very ordered low entropy state, and the temperature difference can be used to power an engine or create electricity. As the air reaches thermal equilibrium, the energy available to do useful work has decreased, until it becomes nothing at all.

This will never spontaneously reverse into useful, hot and cold air again. Unless outside work is put in, like a heat pump. But the work used by the heat pump to create the temperature difference is always going to be more than the work the temperature difference can create. So we always put in more than what we get out. In other words, you can't get something for nothing.

But James Clerk Maxwell didn't like this one bit. He came up with a thought experiment in hope of breaking the second law of thermodynamics. Maxwell's Demon. Maxwell's Demon's only job is to let hot air molecules through to the left side and cold air molecules through to the right. Eventually, there would be all hot air on one side and all cold air on the other.

So where is the increase in entropy coming from? This baffled scientists for over a century. It seems like with information Maxwell's Demon has defied this universal law.

Leo Szilard came along with the answer. The increase in entropy was in the demons brain. To separate the molecules, Maxwell's Demon needs to be constantly measuring molecules, obtaining information and making memories. He uses this information to lower the entropy of the box, but he is using energy to organise information in his brain. Maxwell's demon's brain is also a finite size, and he needs to delete information to make room for more when it gets full. This erasing of information causes heat, entropy increases and the second law of thermodynamics prevails.

So, no, you can't get something for nothing.