# Will the calculated mathematical probability of a decrease of disorder in mixing of gases violate the second law of thermodynamics?

I have read that two different gases mix together when the separation between their chambers is open so as to increase entropy.Similarly the mixed gases won't separate by itself so as to not decrease the disorder.If I were to consider a box with say,90 red balls and 10 blue balls,each with velocities, randomly colliding with itself and the walls of the container,I would expect the blue balls to be mixed with the red balls most of the time but there could be instants of time in which all the blue balls come together due to random collisions.If I were to use the same principle with the case of a mixture of two gases,I expect the theoretical probability for gas molecules to separate on both sides of the container without any external influence to be non zero(however small it is,the probability will be very close to zero).My question is,will that non zero probability violate with the law that disorder or entropy is 'always' increasing?

• No this does not violate the second law, as it is understood since Boltzmann (that is, as a statistical law). There must be many, many questions on this topic on this site. For instance, this one. May 27, 2022 at 6:03