Thermal and configurational entropy

The quantity Q as previously defined ( 11 6) is the number of accessible quantum states of a system. Therefore 2 has a clear meaning only in the case of a system of fixed energy. Now for such a system it was shown in 11 10 that the two entropy analogues 

Of the two formulae above the second has probably the greater intuitive significance, and it was for this reason that it was originally introduced in 1 17. On the other hand, even if we consider systems of fixed energy rather than of fixed temperature, the value of O is usually quite unknown. The advantage of the formulation 

There are, however, certain situations where it is possible to calculate the ratio of fl, as between two states, and therefore the corresponding entropy change. This occurs when the system can exist in a number of geometrical configurations each having the same energy levels. In such instances the use of the expression 

For example, in 1 17 we discussed the mixing of four A atoms with four B atoms on eight lattice sites. The number of configurational states is 

It is evident that this simple result would not have been obtained if were not the same for each of the configurations. However, whenever this condition is satisfied we can write 

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