Grand canonical ensemble

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Ensemble variables

  • Chemical Potential,
  • 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.

Free energy and Partition Function

Free energy and Partition Function

The Helmholtz energy function is related to the canonical partition function via: