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Show from calculating
$$ \frac{\Delta S}{\Delta E}\,=\,\frac{1}{T}\,=\,k\beta$$
for the case of Fermi-Dirac distribution,
$$ \Omega_{FD}\,=\,\Pi_{i=1}^\infty\left({}^{g_i}C_{N_i}\right) $$
[ notation as used in the class ]. Also for the case of equilibrium we have
$$ N_i\,=\,\frac{g_i}{e^{\alpha+\beta\epsilon_i}\,+\,1} $$
Hint: Consider changes only in two levels say with energies $\epsilon _1$ and $\epsilon_2$. Then argue that the result so obtained is independent of the choice of levels]
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5094: SM-HOME, 4727:Diamond Point
