Microcanonical ensemble

The microcanonical ensemble assigns equal probability to accessible states in a narrow energy shell at fixed energy, volume, and particle number.

If $\Omega (E,V,N;\delta E)$ counts states in a narrow experimental energy window, the Boltzmann entropy isChanging the macroscopic resolution $\delta E$ by a fixed factor changes $S$ only by an additive quantity of order $k_B$, whereas $S$ itself is of order $N{k}_B$ in the thermodynamic limit. The dependence on the precise energy-window width is therefore negligible for macroscopic thermodynamics.