I'm reading through Statistical Physics by F. Mandl and in the chapter about the 2nd law of thermodynamics he states that:
The basic distinction between the initial and final states in such an irreversible process is that in the final state we have a less complete knowledge of the state of the system.
Why is this true? Let's say our gas exists in the left side of a container separated by a partition. We know that all the molecules are definitely on the left side.
Now we remove the partition. The gas rushes into the vacuum and eventually spreads itself throughout the container. The book mentions that macroscopic fluctuations of the gas moving around would not be observable unless we waited for a period of time around the order of the age of the universe. So then if we assume that 50% of the gas is on the left side and 50% is on the right side (assume that the partition is infinitesimally thin and unbreakable/unbendable), then how is it that we know less information of the system in this state?