With Boltzmann’s definition in hand, it makes perfect sense that entropy tends to increase over time. The reason is simple: there are far more states with high entropy than states with low entropy. If you start in a low-entropy configuration and simply evolve in almost any direction, your entropy is extraordinarily likely to increase. When the entropy of a system is as high as it can get, we say that the system is in equilibrium. In equilibrium, time has no arrow.
