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| '''Helmholtz energy function''' ([[Hermann Ludwig Ferdinand von Helmholtz]])
| | [[Hermann Ludwig Ferdinand von Helmholtz]] |
| Definition of <math>A</math> (for ''arbeit''): | | Definition of '''A''' (for ''arbeit''): |
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| :<math>A:=U-TS</math> | | :<math>\left.A\right.=U-TS</math> |
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| where ''U'' is the [[internal energy]], ''T'' is the [[temperature]] and ''S'' is the [[Entropy|entropy]]. | | where ''U'' is the [[internal energy]], ''T'' is the [[temperature]] and ''S'' is the [[Entropy|entropy]]. |
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| :<math>\left.A\right.=-k_B T \ln Q_{NVT}</math> | | :<math>\left.A\right.=-k_B T \ln Q_{NVT}</math> |
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| where <math>k_B</math> is the [[Boltzmann constant]], ''T'' is the [[temperature]], and <math>Q_{NVT}</math> is the [[Canonical ensemble | canonical ensemble partition function]].
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| ==Ideal gas==
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| :''Main article: [[Ideal gas Helmholtz energy function]]''
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| ==Quantum correction==
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| A quantum correction can be calculated by making use of the [[Wigner-Kirkwood expansion]] of the partition function, resulting in (Eq. 3.5 in <ref>[http://dx.doi.org/10.1080/00268977900102921 J.G. Powles and G. Rickayzen "Quantum corrections and the computer simulation of molecular fluids", Molecular Physics '''38''' pp. 1875-1892 (1979)]</ref>):
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| :<math>\frac{A-A_{ {\mathrm{classical}} }}{N} = \frac{\hbar^2}{24m(k_BT)^2} \langle F^2 \rangle </math>
| | See also |
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| where <math>\langle F^2 \rangle</math> is the mean squared force on any one atom due to all the other atoms.
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| ==See also==
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| *[[Canonical ensemble]] | | *[[Canonical ensemble]] |
| *[[Grand canonical ensemble]] | | *[[Grand canonical ensemble]] |
| *[[Computing the Helmholtz energy function of solids]]
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| ==References==
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| <references/>
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| [[Category: Classical thermodynamics]] | | [[Category: Classical thermodynamics]] |