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