However, the position of a single particle p0 after 20 seconds is not uniform. It simply doesn’t have time to diffuse far enough; with 2*10^11 collisions and mean free path 70 nm, it will travel a total displacement of 70 nm *sqrt(2*10^11) = 3 cm. Even if the box contains only 1 mol of gas, lower than atmospheric pressure, I think it should only travel 20 cm on average.
It could still be that the total uncertainty in many particles adds up to the majority side being unpredictable.
However, the position of a single particle p0 after 20 seconds is not uniform. It simply doesn’t have time to diffuse far enough; with 2*10^11 collisions and mean free path 70 nm, it will travel a total displacement of 70 nm * sqrt(2*10^11) = 3 cm. Even if the box contains only 1 mol of gas, lower than atmospheric pressure, I think it should only travel 20 cm on average.
It could still be that the total uncertainty in many particles adds up to the majority side being unpredictable.