[[Statistical thermodynamics MOC]]
# Maxwell-Boltzmann statistics

**Maxwell-Boltzmann statistics** is applicable for a system of $N$ identical but distinguishable particles.
The [[Canonical ensemble|canonical partition function]] is given by
$$
\begin{align*}
Z = (Z_{1})^N
\end{align*}
$$
where
$$
\begin{align*}
Z_{1} = \sum_{i} \exp\left( -\frac{\varepsilon_{i}}{k_{B}T} \right)
\end{align*}
$$
is the canonical partition function for a single particle.

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