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>


== Free energy and Partition Function ==
== 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:

  • , 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: