Asymmetry in initial configuration

If we open a valve between a container with a low pressure of a gas and a container with a high pressure of the gas, the gas will expand and fill both containers.

The system evolves towards decreasing the pressure difference essentially because a state with approximately equal pressure is enormously much more probable than a state with a large pressure difference.

However, a state with a small pressure difference is not too improbable compared to a state with zero pressure difference. The random, thermal motion of the molecules may create and subsequently equilibrate small, but not large, pressure differences.

One explanation for irreversibility is that it is a paradox created by our preference for extreme, asymmetric initial states, states which occur at equilibrium with low probability, say 10^{-100000000000}. First we create these wildly unlikely initial states (a compressed gas, a hot cup of coffee, a drop of ink in a glass of water) then we wonder about the decay of these states. If we instead restricted our study to situations which were not too unlikely compared to equilibrium, the paradox is gone.

The idea that asymmetry in the initial conditions is the origin of irreversibility, leads to the correct form for the second law of thermodynamics, SL-IV.