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Canonical ensemble

Spin-1 paramagnet

For $N$ noninteracting units with energies $-\epsilon,0,\epsilon$, put $x=\beta\epsilon$. Then
$$
Z=(1+2\cosh x)^N,
\qquad
E=-\frac{2N\epsilon\sinh x}{1+2\cosh x},
$$
and
$$
S=Nk_B\left[
\log(1+2\cosh x)
-\frac{2x\sinh x}{1+2\cosh x}
\right].
$$


Independent symmetric three-level system

Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 2 / 37A / d / Solution

Independent symmetric three-level system

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Independent symmetric three-level system

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