From Eternity to Here

by Sean Carroll

So this is the origin of the arrow of time, according to Boltzmann and his friends. We start with a set of microscopic laws of physics that are time-reversal invariant: They don’t distinguish between past and future. But we deal with systems featuring large numbers of particles, where we don’t keep track of every detail necessary to fully specify the state of the system; instead, we keep track of some observable macroscopic features. The entropy characterizes (by which we mean, “is proportional to the logarithm of ”) the number of microscopic states that are macroscopically indistinguishable. Under the reasonable assumption that the system will tend to evolve toward the macroscopic configurations that correspond to a large number of possible states, it’s natural that entropy will increase with time. In particular, it would be very surprising if it spontaneously decreased. The arrow of time arises because the system (or the universe) naturally evolves from rare configurations into more common configurations as time goes by.