So I am familiar with the derivation of the partition function for a canonical and a grand canonical ensemble. I have seen definitions of the partition function for some of the quantum counterparts of these. However, I am yet to understand how to write the partition function of a general system.
I've been told that you need to write the energy of a single particle, and take it to the power of N (nr of particles). This only works if the particles are the same tho. What happens if I have some distribution of them?
Let's say my system consists of N particles and M states. The M(1) state can contain let's say 3 particles - degenerate - and corresponds to an energy of E. Let the M(2) state be non-degerative, and let it have energy twice of the first state. And so on, I could define any number os states in any degeneracy, and write all fancy stuff for the energies. Then, let's say every particle interacts with any particle who has energy that is in some range of the given particle. So, all kinds of random rules. How to I write the partition function then?What is the mosz general possible formula for the partition function?