Here is a thought experiment. Imagine a box with 10^20 different particles, all different types of molecules, such that they are not indistinguishable according to QM.
I insert a parition in the middle of the box. Of course since this process is reversible, the entropy is the same. But when I count the number of microstates, every microstate in the new system was also a microstate in the previous system, but the grand majority of the states in the previous system are no longer possible in the partitioned system, since each unique molecule can only be on one side of the partition. To me this seems like a paradox, can someone help me understand why my argument is incorrect?
