Microcanonical Ensemble

#Physics

$\displaystyle {\psi_{i}}:\varepsilon_{1}=\varepsilon_{2}=\varepsilon_{3}=\ldots=\varepsilon$

• The set of all microstates of a system that have the same energy $\displaystyle \varepsilon$
• Each $\displaystyle \psi_{i}$ occur with equal probability

$\displaystyle \psi_{i}(N,V,U)$

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

$\displaystyle P(\varepsilon_{s})=\frac{e^{-\beta\varepsilon_{s}}}{Z}$

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