Does a scientific theory contain more or less information than the experimental evidence on which it's based? If it contains more information, then it must go beyond the evidence that supports it. On the other hand, if it contains less information than the underlying data, what use is it?
``I go to an island where each of the inhabitants is either consistently truthful or a consistent liar. I knock on the door of a house belonging to a man and his wife, and ask, `Are you and your wife truthtellers or liars?'. He shouts, ``We are both liars," and slams the door. What can you deduce about him and his wife?'' (from Raymond Smullyan, Forever Undecided)
Suppose that after a minute, some members of the class have solved this and some have not. Then I tell you the answer. Have I given you any additional information?
Maxwell employed his demon to create a counterexample to the Second Law. The Second Law predicts that entropy cannot spontaneously decrease. To bring about an increase in the order of an isolated system, a certain minimum amount of work must be done. For example, warm water will not spontaneously separate into ice and steam, but we can run a heat pump between two volumes of warm water until one freezes and the other boils. Maxwell's demon disproves the Second Law by producing the same result with arbitrarily little work.
Suppose we have a container holding a mixture of two different kinds of molecule -- these could be two different chemical species, such as oxygen and nitrogen, or molecules of a single gas having high and low speeds respectively. Separating these two kinds of molecule will lead to a reduction in entropy. To separate them, we place a partition across the box, and put a trapdoor in the partition. The trapdoor can be very small -- just big enough that a molecule can pass through -- and very light, so it requires arbitrarily little work to move it. Next to the trapdoor stands the demon. It watches the molecules on either side of the trapdoor, and when it sees a molecule headed for the door, it either opens or closes it, depending on the type of molecule and the direction it's coming from. In this way the gas will eventually be sorted into one kind of molecule on one side of the partition, the other kind on the other side.
Maxwell argued as follows:
``One of the best-established facts in thermodynamics is that it is impossible in a system enclosed in an envelope which permits neither change in volume nor passage of heat, and in which both temperature and pressure are everywhere the same, to produce any inequality of temperature or pressure without the expenditure of work. This is the second law of thermodynamics, and it is undoubtedly true as long as we can deal with bodies only in mass and have no power of perceiving or handling the separate molecules of which they are made up. But if we conceive a being whose faculties are so sharpened that he can follow every molecule in its course, such a being, whose attributes are still as essentially finite as our own, would be able to do what is at present impossible for us. For we have seen that the molecules in a vessel full of air at uniform temperature are moving with velocities by no means uniform, though the mean velocity of any great number of them, arbitrarily selected, is almost exactly uniform. Now let us suppose that such a vessel is divided into two portions A and B by a division in which there is a small hole, and that a being who can see the individual molecules opens and closes this hole, so as to allow only the swifter molecules to pass from A to B and only the slower ones to pass from B to A. He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics." [J.C. Maxwell, ``Theory of Heat," Longmans, Green, London, pp. 338-339, 1891.]
We might imagine replacing the demon by a nanomachine, of the kind discussed in Lecture 11. If this is possible, it would allow us to build machines which could generate work from a single source of heat -- for example, we could take a bucket of seawater, use a demonic nanomachine to convert it to ice and steam, then run a heat engine between ice and steam temperatures. No new energy would be created, but we could continually re-use the energy that was degraded to heat.
Is the creation of such a nanomachine in fact possible? If not, why not? [The resource file ``Second Law and Computing'' may be helpful.]