1. The problem statement, all variables and given/known data If we have a system of N independent particles and the partition function for one particle is Z_1, then is the partition function for the N particle system Z=(Z_1)^N? 2. Relevant equations 3. The attempt at a solution I'm pretty sure that this is true for a classical system, but I'm not sure if it's true for a quantum system. Does the Pauli exclusion principle spoil this somehow?