I have a few doubts about the canonical ensemble. Let's consider a system A in contact with a heat reservoir.
1) To derive the probability of the system being in a state $E_r$, we consider the probability of the reservoir being in the state $E_t$ - $E_r$ where $E_t$ is the total energy of the system.Then we try to find that $E_r$ where the number of states of the reservoir is maximum.While this is fine for small systems, what do you do for larger systems?(You have to also start considering the number of states of the system at some point,right?)
2)The reservoir has a very large heat capacity and a very large number of degrees of freedom. Does this always mean it is physically larger than the system?