Microcanonical Ensemble

$\{{\psi }_i\}:{\epsilon }_1={\epsilon }_2={\epsilon }_3=\dots =\epsilon$

• The set of all microstates of a system that have the same energy $\epsilon$
• Each ${\psi }_i$ occur with equal probability

${\psi }_i(N,V,U)$

• Assumes constant number of particles $N$, volume $V$, and energy of the system $\epsilon$

$P({\epsilon }_s)=\frac{e^{-\beta {\epsilon }_s}}{Z}$

• Boltzmann distribution for microcanonical ensemble
• Probability of a system occupying a state $s$ with energy ${\epsilon }_s$. A state $s$ may refer to the spin of the spin magnet system for example
• $\beta$ is [coldness] of the system
• $Z$ is the [partition function]