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We know how to calculate mean energy. How can we calculate mean
*entropy* ?

Consider a *macroscopic* state with energy *E* in canonical
ensemble:

Additivity of entropy:

*S*_{A} = *S*_{M} - *S*_{B}

We obtained:

Average entropy:

Since , we obtained:

*A* = *E* - *TS*

Suppose we have a function *f*(*x*). New variables:

*g*'(*p*) = -*x*

Example: Hamilton & Lagrange Mechanics.

Free energy is Legendre transformation of energy (or entropy). In particular

It means that© 1997

Tue Sep 9 22:39:08 EDT 1997