Grand canonical ensemble
Ensemble variables
- Chemical Potential,
- Volume,
- Temperature,
Partition Function
Classical partition function (one-component system) in a three-dimensional space:
where:
- is the number of particles
- is the de Broglie thermal wavelength (which 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 position coordinates of the particles (reduced with the system size): i.e.
Free energy and Partition Function
(THis subsection should be checked)
The corresponding thermodynamic potentail for the grand canonical partition function is:
- , i.e.: