Helmholtz energy function
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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:
where kB is the Boltzmann constant, T is the temperature, and QNVT is the canonical ensemble partition function.
