Can we talk about the chemical potential of a system with fixed number of particles? Is this physically meaningful? Why/why not? P.s: I know that chemical potential is the partial derivative of free energy with respect to number of particles. But in the formulation of grand canonical ensemble, we write N=Ʃf (for example f would be fermi-dirac distribution function) and can't we fix N in this formula, and solve chemical potential μ by changing energy ε?