Problem

Order Out of Chaos The second law of thermodynamics specifies that “the future”...

Order Out of Chaos

The second law of thermodynamics specifies that “the future” is the direction of entropy increase. But, as we have seen, this doesn’t mean that systems must invariably become more random. You don’t need to look far to find examples of systems that spontaneously evolve to a state of greater order.

A snowflake is a perfect example. As water freezes, the random motion of water molecules is transformed into the orderly arrangement of a crystal. The entropy of the snowflake is less than that of the water vapor from which it formed. Has the second law of thermodynamics been turned on its head? The entropy of the water molecules in the snowflake certainly decreases, but the water doesn’t freeze as an isolated system. For it to freeze, heat energy must be transferred from the water to the surrounding air.

The entropy of the air increases by more than the entropy of the water decreases. Thus the total entropy of the water + air system increases when a snowflake is formed, just as the second law predicts. If the system isn’t isolated, its entropy can decrease without violating the second law as long as the entropy increases somewhere else.

Systems that become more ordered as time passes, and in which the entropy decreases, are called self-organizing systems. These systems can’t be isolated. It is common in self-organizing systems to find a substantial flow of energy through the system. Your body takes in chemical energy from food, makes use of that energy, and then gives waste heat back to the environment. It is this energy flow that allows systems to develop a high degree of order and a very low entropy. The entropy of the environment undergoes a significant increase so as to let selected subsystems decrease their entropy and become more ordered.

Self-organizing systems don’t violate the second law of thermodynamics, but this fact doesn’t really explain their existence. If you toss a coin, no law of physics says that you can’t get heads 100 times in a row—but you don’t expect this to happen. Can we show that self-organization isn’t just possible, but likely?

Let’s look at a simple example. Suppose you heat a shallow dish of oil at the bottom, while holding the temperature of the top constant. When the temperature difference between the top and the bottom of the dish is small, heat is transferred from the bottom to the top by conduction. But convection begins when the temperature difference becomes large enough. The pattern of convection needn’t be random, though; it can develop in a stable, highly ordered pattern, as we see in the figure. Convection is a much more efficient means of transferring energy than conduction, so the rate of transfer is increased as a result of the development of these ordered convection cells.

The development of the convection cells is an example of self-organization. The roughly 1023 molecules in the fluid had been moving randomly but now have begun behaving in a very orderly fashion. But there is more to the story. The convection cells transfer energy from the hot lower side of the dish to the cold upper side. This hot-to-cold energy transfer increases the entropy of the surrounding environment, as we have seen. In becoming more organized, the system has become more effective at transferring heat, resulting in a greater rate of entropy increase! Order has arisen out of disorder in the system, but the net result is a more rapid increase of the disorder of the universe.

Convection cells are thus a thermodynamically favorable form of order. We should expect this, because convection cells aren’t confined to the laboratory. We see them in the sun, where they transfer energy from lower levels to the surface, and in the atmosphere of the earth, where they give rise to some of our most dramatic weather.

Self-organizing systems are a very active field of research in physical and biological sciences. The 1977 Nobel Prize in chemistry was awarded to the Belgian scientist Ilya Prigogine for his studies of non-equilibrium thermodynamics, the basic science underlying self-organizing systems. Prigogine and others have shown how energy flow through a system can, when the conditions are right, “bring order out of chaos.” And this spontaneous ordering is not just possible—it can be probable. The existence and evolution of self-organizing systems, from thunderstorms to life on earth, might just be nature’s preferred way of increasing entropy in the universe.