## probability forms of entropy

Posted by peeterjoot on March 16, 2013

## Question: Entropy as probability

[1] points out that entropy can be written as

where

Show that this follows from the free energy .

## Answer

In terms of the free and average energies, we have

## Question: Entropy in terms of grand partition probabilites ( [2] pr 4.1)

Generalize \cref{pr:entropyProbabilityForm:1} to the grand canonical scheme, where we have

and show

## Answer

With

the free energy takes the form

so that the entropy (scaled by ) leads us to the desired result

# References

[1] E.A. Jackson. *Equilibrium statistical mechanics*. Dover Pubns, 2000.

[2] RK Pathria. *Statistical mechanics*. Butterworth Heinemann, Oxford, UK, 1996.

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