A Guide to Physics Problems. Part 2. Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 213

Therefore, comparing (S.4.93.4) and (S.4.93.5), we deduce that, at constant

volume,

or in standard units

Since

then

Second solution: A more general approach may be followed which is appli-

cable to other problems. Because the probability of finding that the value

of a certain quantity X deviates from its average value is proportional

to and denoting we can write

Note that The entropy has a maximum at Expanding

where

so The probabilitydistribution

If we have several variables,

If the fluctuations of two variables are statistically independent,

we obtain

so