Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 215

where we used

So, finally

Using V and as independent variables we have

Substituting (S.4.93.19) into (S.4.93.18), we see that the cross terms with
cancel (which means that the fluctuations of volume and temper-
ature are statistically independent,

Comparing (S.4.93.20) with (S.4.93.10), we find that the fluctuations of
volume and temperature are given by

To find the energy fluctuation, we can expand