The Bayesian Second Law of Thermodynamics – Sean Carroll

Entropy increases. Closed systems become increasingly disordered over time. So says the Second Law of Thermodynamics, one of my favorite notions in all of physics. At least, entropy usually increases. If we define entropy by first defining “macrostates” — collections of individual states of the system that are macroscopically indistinguishable from each other — and then taking the logarithm of the number of microstates per macrostate, as portrayed in this blog’s header image, then we don’t expect entropy to always increase. According to Boltzmann, the increase of entropy is just really, really probable, since higher-entropy macrostates are much, much bigger than lower-entropy ones. But if we wait long enough — really long, much longer than the age of the universe — a macroscopic system will spontaneously fluctuate into a lower-entropy state. Cream and coffee will unmix, eggs will unbreak, maybe whole universes will come into being. But because the timescales are so long, this is just a

saved by

• Christian Larsen