We consider again the system in Exercises 1 and 2 and make use of the same notation.

Question:

We consider again the system in Exercises 1 and 2 and make use of the same notation.
We will study the limits T → 0 and T →∞.

(a) In the limit T → 0 compute the four probabilities given by Eq. (6.7) and compute
directly the entropy in Eq. (6.11) in this limit.

Equation (6.11)

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Equation (6.7)

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(b) In the limit T →∞compute the four probabilities given by Eq. (6.7) and compute
directly the entropy in Eq. (6.11) in this limit.

Equation (6.11)

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Equation (6.7)

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(c) Now use the expression valid for all temperatures in Eq. (6.121) and from this
expression derive the limting values of (a) and (b).


Equation (6.121)

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