Microcanonical energy-shell entropy ($S(E,V,N)=k_B\log \Omega (E,V,N;\delta E)$)

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.