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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
Additivity of entropy:
SA = SM - SBProbability of a microscopic state in canonical ensemble:
Since , we obtained:
A = E - TSWe know that
and since ,
Suppose we have a function f(x). New variables:
Consider the function
We see that:
g'(p) = -xThe function g is Legendre transformation of the function f.
Example: Hamilton & Lagrange Mechanics.
Free energy is Legendre transformation of energy (or entropy). In particular
It means that A=A(T,V)
© 1997 Boris Veytsman and Michael Kotelyanskii