I've always been slightly confused by the Second Law of Thermo. For example, with Maxwell's Demon, where a demon controls the partition between two gas chambers to select all the fast moving particles into one chamber, the Second Law is not violated because the demon's actions and thought process increases entropy. However, say that the demon was removed. By pure random chance, isn't it entirely possible that the fast, hot particles will move into one chamber and the cold, slow particles will move into the other chamber? All textbooks/guides/videos say that yes, it is possible, but the chances are extremely small. Thus, when this situation actually happens after a very long time, entropy decreases, so isn't this a direct violation of the Second Law of Thermo? Assuming that the system is in an isolated vacuum, this also means that there can be no transfer of heat to the surroundings, so there is nothing else that can gain entropy. How is my thought process incorrect? Thanks!