William Dembski has used the term “4th law of thermodynamics” to describe the law of conservation of information. For this he was savaged by the Darwinian fanatics who suggested that postulating a new law of nature was insane.
But here is philosopher Wallace I. Matson who in a 1965 book The Existence of God gave an example similar to one Dembski used to illustrate the law:
A common example of increase of entropy is the diffusion of liquids.
Half fill a beaker with water and then very carefully pour red wine into the upper half. There will then be two layers, the bottom one colorless and the top one red. If the beaker is left undisturbed, in time the differentiation will vanish; a uniformly pink fluid will be found in it.
This is because the molecules of water and wine at the boundary are in constant random motion, some up, some down. The molecules of wine will pass into the water, and vice versa. The process is not reversible…
But suppose now that a solid disc is placed horizontally in the middle of the beaker. There is a hole in it just big enough to allow a single molecule to pass; and the hole is provided with a cover. This cover is held by an infinitesimal but intelligent being (“Maxwell’s demon”) who is able to distinguish water molecules from wine molecules, as in their random motion they approach the hole.
Whenever he sees a wine molecule approaching from below, or a water molecule from above, he opens the hole and lets the molecule pass through; otherwise he keeps it shut. In this way, the mixture might separate itself (for the demon does not shove any of the molecules; he does no work on this isolated system), and its entropy might decrease under the guidance but not added physical energy of an intelligence. (Critiques of God, 79)
Matson then objects that human intelligence is embodied, and so the 4th law is not by that fact an exception to the 2nd law. There may be something to this objection, but the point is this: as long as an intelligent agent has certain true beliefs, however acquired, then he may be able to costlessly decrease the entropy in a system.
It may be that in order to obtain those true beliefs, such as which molecules are water and which are wine, an embodied intelligence must expend energy and in the end increase overall entropy, with the upshot that “there is no ‘anabolic and antientropic factor of whose existence we are certain in ourselves.'” But an ideal mind is immaterial, as for that matter is God. Hence the argument works, and Dembski is correct.