**Definition 0.0.1 **  The **microcanonical ensemble** is the ensemble of statistical mechanics where the macrostates are described by the energy $E$, volumes $\mathbf{V}$ and particle numbers $\mathbf{N}$.
\[\mathscr{p}_i = \frac{1}{\Omega(E,\mathbf{V},\mathbf{N})}\]