In looking at phonons, and their energy, I came across the Partition function. THis was needed to calculate the internal energy of the solid. But howcome the Partition fucntion is used, and not the GRAND Partition function? The number of phonons is not conserved, I know that, but isn't N, the number, fixed in the Partition function??? Surely one should used the GPF to take into acount the varying number?? I guess I have misunderstood something here. Any help appreciated!!