Maxwell's Demon

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Maxwell's Demon

Postby hyksos on September 20th, 2018, 2:35 am 

Maxwell's Demon is a thought-experiment in which we construct a machine that can harvest infinite amounts of energy. The M-D raises serious questions about the relationship between quantum mechanics, thermodynamics, and information preservation.

A Maxwell Demon is device that watches warm air molecules in two chambers. The demon selectively opens and closes a door between them so that warm particles end up in the lefthand chamber and cooler ones collect in the righthand side. After a while, a temperature difference exists, and that difference could drive an engine to charge a battery. The device could repeat the procedure as many times as it wants, extracting more energy at each stage.

On most internet venues, it is sufficient to merely point out that you are suggesting perpetual motion, then declare that impossible and end the conversation. A much more interesting question would be : given the known laws of physics why is the M-D impossible?

My understanding of this problem is that it is related to the fact that the Demon itself must perform computation, and if it does so, it must destroy information by switching a transistor. The switching of a single bit in an idealized computer cannot be performed for zero energy, so the Demon must be attached to some outside power source.

The switching of a single bit in a register of a computer could overwrite information there, and as far as we know, the energy expended from losing a single bit of information is determined by Landau's Limit, given as

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E = k T ln 2

T is the temperature of the surrounding environment (the "heat sink" in other words). k is Boltzman's constant.

If there was an equals sign in there anywhere (>=) the equals situation would imply the existence of a perpetual motion machine, which is forbidden. Applying the 2nd Law of Thermo, the equation turns into an inequality, and we can express the amount of energy the Demon will "use up" and give back to the environment as heat as

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H(B) > B k T ln 2

Where B is the number of bits lost by a computation.

Ocean water contains gold in it. It is very small but non-zero. One might ask why we are not all rich already. The cost of extraction of gold from seawater outweighs the money gained from selling the gold. It is economically infeasible.

A similar analogy happens with the Maxwell Demon. While no apparent principle of physics are violated by the Demon (in other words, it should work given all we know) if you take into account the energy expended by the demon's "mind" you do not break even. So while a Maxwell Demon can be constructed in a laboratory -- and several have been -- and they work at isolating hotter particles into one chamber, and cooler particles into another, a consideration of the entire laboratory would never yield a net energy increase.
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Re: Maxwell's Demon

Postby dandelion on September 22nd, 2018, 3:41 am 

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Re: Maxwell's Demon

Postby phyti on September 22nd, 2018, 10:45 am 

It requires energy to operate the door!
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