Example 5.8: Mean square deviation of energy Show that the mean square deviation of the energy E, i.e.

(E)2 = (E − E)2 = E2 − E 2

, (5.69)

is given by

(E)2 =

∂2 lnZ

∂β2

= −

∂E

∂β

, β=

1 kT