The 2nd law of thermodynamics state that entropy increases with time and entropy is just a measure of how hard it is to distinguish a state from another state (information theoretical view) or how hard it is to find order within a system (thermodynamic view). There are many ways to view entropy but these are the two that I find most pleasing and they are actually equivalent. Let's consider a box with 2 kinds of identical but distinguishable (but enough to interfere with the interactions) gas molecules which are initially separated; after a while they mix and become more disorderly due to the random motion of molecules. This seems to agree with the 2nd law of thermodynamics. But, after a very long time, the randomness would eventually create a fluctuation where the gas would unmix and lead back to the initial state; where they are separated. Does this mean that entropy could decrease after a long time?