I was learning about the "Many Worlds" interpretation of QM, and it got me to thinking. In some ways, doesn't it contradict the laws of thermodynamics? I came up with the following thought experiment: Suppose that you had a gas containing nitrogen and oxygen in a homogeneous mixture, in a container separated by a porous membrane. Now, I'm assuming that in each collision, the final positions and velocities of each molecule is at least somewhat determined by the instantaneous position of the molecules' electrons at the time of the collision. That means that there is a slight (nearly infinitesmal) possibility that all of the nitrogen will end up on one half of the membrane, and that all of the oxygen will end up on the other half. Now, since the probability is not zero, according to the Many Worlds interpretation of QM, there are at least a handful of universes in which this will indeed happen. Therefore, this means that the entropy of those universes has in fact decreased. Now, I was under the impression that the laws of physics of the every universe would be the same, and as a result, the entropy should not ever decrease. Isn't this an inherent contradiction?