Microcanonical Ensemble

Fixed Energy

The microcanonical ensemble describes an isolated system with fixed $E,V,N$. Allowed microstates compatible with the macroscopic constraints are assigned equal probability.

Entropy

If $\Omega(E,V,N)$ is the number of accessible states, the entropy is

$$S=k_B\ln\Omega.$$

Temperature is then defined by

$$\frac{1}{T}=\left(\frac{\partial S}{\partial E}\right)_{V,N}.$$