Helmholtz energy function

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Helmholtz energy function (Hermann Ludwig Ferdinand von Helmholtz) Definition of (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 is the Boltzmann constant, T is the temperature, and is the canonical ensemble partition function.

Ideal gas

Main article: Ideal gas Helmholtz energy function

Quantum correction

A quantum correction can be calculated by making use of the Wigner-Kirkwood expansion of the partition function, resulting in (Eq. 3.5 in [1]):

where is the mean squared force on any one atom due to all the other atoms.

See also

References