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[edit]

Main article: Ideal gas Helmholtz energy function

Quantum correction[edit]

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[edit]