Entropy Explained (2003, 2005)
Addendum A to "Bad Science, Worse Philosophy: the Quackery and Logic-Chopping of David Foster's The Philosophical Scientists" (2000)
In traditional thermodynamics, entropy is a measure of the amount of energy in a closed system that is no longer available to effect changes in that system. A system is closed when no energy is being added to or removed from it, and energy becomes unavailable not by leaving the system, but by becoming irretrievably disordered, as a consequence of the laws of statistical mechanics. But even though the total amount of energy that is irretrievably disordered will increase, this does not mean order cannot increase somewhere else in that same system. This is where confusion arises. Of course, entropy can be measured in an open system, too, but this introduces additional variables, and of course the Second Law then no longer applies. But even when the Second Law applies, it is still possible for a closed system to produce order, even highly elaborate order, so long as there is a greater increase in disorder somewhere else in the system.
Consider, for example, how the atmosphere remains attached to earth in an orderly sphere rather than just wandering off at random. In fact, though a layman would say this system is highly ordered and doesn't become notably disordered over time (billions of years and the air is still here), the entropy of this system does increase: though a relatively orderly arrangement of gases around earth is also produced, at the same time a large quantity of energy has become disordered as a result. For example, friction created by the impact of these gas molecules striking the earth and each other produces heat that ultimately radiates off into space. Thus, the Second Law is conserved: the total amount of disordered energy is increased, even as a visible increase in order is produced. Thus, though an increase in entropy entails an increase in disorder, it does so only overall, and therefore as long as the amount of energy that becomes ordered is less than the amount of energy that becomes disordered, any amount of order can arise in a closed system without violating the Second Law. The natural universe is filled with examples of local order being produced by increasing overall entropy: the structure of atoms has this effect on crystalization, the nature of subatomic particles has an ordering effect on the sorts of molecules that can form, and so on. In fact, the whole of chemistry, the foundation of life, is an ideal example. Hence the Second Law cannot be invoked against a natural origin of life, since under certain conditions there can be a significant increase in order while the total amount of disordered energy also increases.
Seen on a cosmic scale, although an increase in entropy entails an increase in the quantity of energy in the universe that is irretrievably disordered, this is not the same thing as a tendency toward disorder everywhere in the universe, since the rest of the energy in the universe still has to be accounted for, and could behave in any number of ways, depending on the forces and structures found there. Of course, though in a closed system the quantity of energy that is irretrievably disordered increases, that very same energy can be reordered by an expenditure of new energy introduced to the system. Or by allowing some of the disordered energy to escape a system, the entropy of that system can be made to decrease. But either way, we still increase the quantity of disordered energy in the universe, and so far as we know it can never be otherwise. Thus, the total amount of order in the universe will certainly decrease (though due to the Third Law it will never disappear entirely), yet even as this happens, parts of the universe can continue to become more orderly without violating the Second Law.
In fact, order can only be produced by increasing entropy. This is because producing order out of chaos involves a change in the system, which can only be produced by expending energy. The expenditure of energy is never perfectly efficient and so it always increases the overall amount of energy that is irretrievably disordered, even as order is produced from the remaining energy. Since ordering requires an increase in entropy, it is a bit ironic to find creationists claiming entropy as an anti-ordering process (which it is not) in order to "prove" special creation, when it would make more sense to use it as an ordering process to "prove" divine arrangement of the laws of physics. However, I must head off such a switch-hitting strategy. There is no sign of intelligent design in the Second Law. It is actually the only logical way that any mindless, material universe would operate. Since it is the logically necessary result of any universe which contains bits of mass-energy that never change in quantity, all that is needed for this law to materialize is such a universe, leaving no room for any intelligent tinkering--except at the point of the creation of those bits of stuff or the space and time in which they move, but that is another story. When we examine the Second Law alone, we see that it would be the natural result of any undesigned but merely existing universe, which contained an unchanging quantity of bits. At the same time, we see that this law prevails over and defines every change in the universe we happen to be in, and yet in no way prevents natural order from arising--so long as energy becomes disordered in producing it.
 The present article has been rewritten several times, since in past incarnations it confused many readers. Hopefully it is finally in a simpler form that is clear enough to everyone. For further discussion see Dr. Frank Lambert's Entropy Is Simple (which covers almost all the important issues surrounding entropy) and Brig Klyce's The Second Law of Thermodynamics (which analyzes how physicists have misled laymen with their sloppy writing).
 See John Baez, Can Gravity Decrease Entropy? (2000). Of course, the real earth is not a closed system (e.g. it receives radiation from the sun), but this analogy imagines an earth alone in the middle of an otherwise-empty space randomly filled with gas.
 For example, see Another Face of Entropy: Particles Self Organize to Make Room for Randomness," Science News 154:7 (August 15, 1998), pp. 108-9: when large and small molecules of microscopic but not quite atomic scale are mixed at random, order naturally results, in contravention of the popular (and mistaken) idea of the Law of Entropy. However, the phenomenon still obeys the actual Law, because the system increases the entropy of the small molecules while decreasing the entropy of the large ones, and the sum result is an increase in entropy.
 For more on the origin of life, see Are the Odds against the Origin of Life Too Great to Accept?.