Canonical ensemble: Difference between revisions
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* <math> \left( R^*\right)^{3N} </math> represent the 3N position coordinates of the particles (reduced with the system size): i.e. <math> \int d (R^*)^{3N} = 1 </math> | * <math> \left( R^*\right)^{3N} </math> represent the 3N position coordinates of the particles (reduced with the system size): i.e. <math> \int d (R^*)^{3N} = 1 </math> | ||
== | == Helmholtz energy and partition function == | ||
The [[Helmholtz energy function]] is related to the canonical partition function via: | The [[Helmholtz energy function]] is related to the canonical [[partition function]] via: | ||
:<math> A\left(N,V,T \right) = - k_B T \log Q_{NVT} </math> | :<math> A\left(N,V,T \right) = - k_B T \log Q_{NVT} </math> | ||
[[Category:Statistical mechanics]] | [[Category:Statistical mechanics]] |
Revision as of 16:25, 5 March 2007
Variables:
- Number of Particles,
- Volume,
- Temperature,
Partition Function
Classical Partition Function (one-component system) in a three-dimensional space:
where:
- is the de Broglie thermal wavelength (depends on the temperature)
- , with being the Boltzmann constant
- is the potential energy, which depends on the coordinates of the particles (and on the interaction model)
- represent the 3N position coordinates of the particles (reduced with the system size): i.e.
Helmholtz energy and partition function
The Helmholtz energy function is related to the canonical partition function via: