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
- , 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.
Helmholtz energy and partition function
The corresponding thermodynamic potential, the grand potential, ,
for the grand canonical partition function is:
- ,
where A is the Helmholtz energy function.
Using the relation
one arrives at
i.e.: