Helmholtz energy function

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Hermann Ludwig Ferdinand von Helmholtz Definition of A (for arbeit):

where U is the internal energy, T is the temperature and S is the entropy. (TS) is a conjugate pair. The differential of this function is

From the Second law of thermodynamics one obtains

thus one arrives at

.

For A(T,V) one has the following total differential

The following equation provides a link between classical thermodynamics and statistical mechanics:

See also the Canonical ensemble.