Lectures 2 and 3: Evolution, Entropy, and non-equilibrium thermodyamics

Creationists often argue that the 2nd law of thermodynamics, that is, that the entropy of a system increases over time, precludes the whole idea of evolution, which would seem to require that order and complexity develop from disorder. Their argument, of course, is easily dismissed by noting that the law only states that the entropy of a closed system will increase over time, and the Earth is anything but a closed system - witness that giant flaming ball that hangs inconveniently overhead right around noon. But what's even more powerful is to note that pockets of order can arise spontaneously, even when the entropy of a closed system must increase overall.

Thermodynamics, strictly speaking, only applies to systems in equilibrium. For example, if we consider ice in a glass of water, the system bounded by the glass will have reached equilibrium once the ice melts and the system is at rest. That is, if we zoom in to all the water molecules zipping and crashing about, we'd find that statistically the net molecular velocity of the system is zero. This is in fact what is meant by temperature - only a meaningful concept when the system is in equilibrium.

There are a number of systems, though, that are highly ordered but NOT in equilibrium. For example, take a pot, fill it with a thin layer of water, and put it on a stove. Heat flows from the bottom of the water to the top, generating a temperature gradient. For moderate gradients, the net velocity of the water molecules remains zero (at a single time instant - obviously the temperature increases with time). With larger temperature gradients, though, hexagonal convection cells form as if the water were a crystal. They are quite orderly. As another example, take a fluid at rest. It is orderly and looks the same in all directions - isotropic. As you force this fluid through a metal grid, though, it starts to become turbulent on its downstream side - no longer isotropic. However, as you increase the flow even more, the turbulence pervades the entire liquid, which now no longer flows in a single direction - it is in a sense equally turbulent in all directions, and back to isotropic. Thus, the liquid has progressed from ordered to disordered back to ordered. Similar examples of order arising from chaos include vortices and hurricanes.

Standard thermodynamics, because it only applies to equilibrium systems, does not capture the above phenomena. But another branch of thermodynamics called non-equilibrium thermodynamics does. This describes how order and disorder can fluctuate within a system and how order and complexity can develop spontaneously, even within the closed system of a chemical reaction. "Islands" of order within small systems are sometimes MORE probable than generalized disorder, even though the overall entropy of the system increases. Might this raises some interesting possibilities for the evolution of life?