From Eternity to Here

by Sean Carroll

So the largest conceivable change in entropy that would be required to take a completely disordered collection of molecules the size of our biomass and turn them into absolutely any configuration at all—including the actual ecosystem we currently have—is 1044. If the evolution of life is consistent with the Second Law, it must be the case that the Earth has generated more entropy over the course of life’s evolution by converting high-energy photons into low-energy ones than it has decreased entropy by creating life. The number 1044 is certainly an overly generous estimate—we don’t have to generate nearly that much entropy, but if we can generate that much, the Second Law is in good shape. How long does it take to generate that much entropy by converting useful solar energy into useless radiated heat? The answer, once again plugging in the temperature of the Sun and so forth, is: about 1 year. Every year, if we were really efficient, we could take an undifferentiated mass as large as the entire biosphere and arrange it in a configuration with as small an entropy as we can imagine. In reality, life has evolved over billions of years, and the total entropy of the “Sun + Earth (including life) + escaping radiation” system has increased by quite a bit. So the Second Law is perfectly consistent with life as we know it—not that you were ever in doubt.