Comparison of statistical analogues with thermodynamic functions

Comparison of statistical analogues with thermodynamic functions 

Therefore, if we identify S with S and A with A, we must have 

That this is not unsatisfactory may be seen by returning to the discussion following equation (11 9). It was shown that fi is normally a negative quantity and also that it has the same value for any two bodies which are in equilibrium in a heat bath. The statistical quantity fi is therefore a function of the thermodynamic temperature. Equation (11 34) is clearly consistent with everything that has been established so far. 

A more complete identification of the statistical with the thermodynamic quantities can be carried out if we make use of a result from wave mechanics, namely, that the energies Ei depend only on the 

Now whenever there is a state of equilibrium with a heat bath, the P, are given by 

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