= Microcanonical energy-shell entropy
{title2=$S(E,V,N)=k_B\log\Omega(E,V,N;\delta E)$}
If $\Omega(E,V,N;\delta E)$ counts states in a narrow experimental energy window, the <Boltzmann entropy> is
$$
S(E,V,N)=k_B\log\Omega(E,V,N;\delta E).
$$
Changing 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 $Nk_B$ in the <thermodynamic limit>. The dependence on the precise energy-window width is therefore negligible for macroscopic thermodynamics.
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