For a classical system containing $r$ discrete energy levels and $N$ indistinguishable particles, the total number of possible microstates is simply $r^N$, but what is the number of possible marcostates? Can this even be determined from a simple formula?
To illustrate, suppose I have a system with 2 energy states and 4 particles. The total number of microstates is $2^4 = 16$, while the total number of macrostates is 5:
- State I: 4 particles in level 1 & 0 particles in level 2.
- State II: 3 particles in level 1 & 1 particle in level 2.
- State III: 2 particles in level 1 & 2 particles in level 2.
- State IV: 1 particle in level 1 & 3 particles in level 2.
- State V: 0 particles in level 1 & 4 particles in level 2.
Is there a formula that tells us that the number of macrostates is 5?
