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. Does this imply that macroscopic phenomena are also reversible? Consider an isolated many-particle system that 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 in time then the system will appear to evolve away from equilibrium, and the quantity $H$ will increase. This type of behavior is not physical because it violates the $H$ -theorem. In other words, if we saw a film of a macroscopic process then 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 appears completely unphysical. We would start off from perfectly normal air, and suddenly, for no good reason, the air's constituent 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 appear unphysical 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 intermingled by continually scattering off one another. Each individual scattering event would look perfectly reasonable viewed in reverse. However, the net result of these scattering event appears unphysical when run backwards. 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. (We shall answer the question in Section 5.6.) Note, however, that the essential irreversibility of macroscopic phenomena is one of the key results of statistical thermodynamics.