Definition 0.0.1  A classical ideal gas in the microcanonical ensemble is the system with hamiltonian $\mathcal{H}$ defined by
$$\mathcal{H}=\sum _{i=1}^N\frac{{\mathbf{p}}_i^2}{2m}$$$$\mathrm{\Omega }\approx \frac{2{\pi }^{3N/2}}{(3N/2-1)!}\frac{2m^{3N/2}}{N!(2\pi \hslash {)}^{3N}3N}\frac{3N\mathrm{\Delta }}{2E}{V}^N{E}^{3N/2}$$