Reversibility and irreversibility

Previously, we mentioned that on a microscopic level the laws of physics are invariant under time reversal. In other words, microscopic phenomena look physically plausible when run in reverse. We usually say that these phenomena are reversible. What about macroscopic phenomena? Are they reversible? Well, consider an isolated many particle system which starts off far from equilibrium. According to the $H$ theorem, it will evolve towards equilibrium and, as it does so, the macroscopic quantity $H$ will decrease. But, if we run this process backwards the system will appear to evolve away from equilibrium, and the quantity $H$ will increase. This type of behaviour is not physical because it violates the $H$ theorem. So, if we saw a film of a macroscopic process we could very easily tell if it was being run backwards. For instance, suppose that by some miracle we were able to move all of the Oxygen molecules in the air in some classroom to one side of the room, and all of the Nitrogen molecules to the opposite side. We would not expect this state to persist for very long. Pretty soon the Oxygen and Nitrogen molecules would start to intermingle, and this process would continue until they were thoroughly mixed together throughout the room. This, of course, is the equilibrium state for air. In reverse, this process looks crazy! We would start off from perfectly normal air, and suddenly, for no good reason, the Oxygen and Nitrogen molecules would appear to separate and move to opposite sides of the room. This scenario is not impossible, but, from everything we know about the world around us, it is spectacularly unlikely! We conclude, therefore, that macroscopic phenomena are generally irreversible, because they look ``wrong'' when run in reverse.

How does the irreversibility of macroscopic phenomena arise? It certainly does not come from the fundamental laws of physics, because these laws are all reversible. In the previous example, the Oxygen and Nitrogen molecules got mixed up by continually scattering off one another. Each individual scattering event would look perfectly reasonable viewed in reverse, but when we add them all together we obtain a process which would look stupid run backwards. How can this be? How can we obtain an irreversible process from the combined effects of very many reversible processes? This is a vitally important question. Unfortunately, we are not quite at the stage where we can formulate a convincing answer. Note, however, that the essential irreversibility of macroscopic phenomena is one of the key results of statistical thermodynamics.