How to break the second law of thermodynamics?

On the mind demons…

To put things in order, as is well known, you need to do some work. In thermodynamics, this (second) law is expressed in the fact that the disorder of molecule motion in a container with gas, entropy, does not decrease if there is no external impact. However, James Maxwell who was the first to write the formula of electromagnetism allowed himself to doubt it, imagining that the container is divided by a wall with a hole which can be closed by the fancy finite being that Lord Kelvin has called Maxwell’s demon. Should the demon allow the faster molecules to pass through the hole just to the right of the wall, and the slower ones — to the left, then the average velocity of the molecules to the right will increase soon and there will be warmer, there will be greater order in the container and, therefore, the entropy will decrease. This would violate the second law of thermodynamics, unless it is difficult for the demon to sort molecules, i.e., if it does almost no work. Over the years it was realized that the demon should record the results of measurements of each molecule’s speed, so that sooner or later its ‘disk drive’ is full and it begins to erase the information, which will lead to an increase of entropy and compensate for its decline in the container. About 140 years later, in the XXI century, the nano-devices have been created, which carry out the demon functions.

Maxwell's demon restores order in a container with gas

To sort gas molecules over velocities, Maxwell’s demon would have to do measurements and book-keeping.

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