# Canonical ensemble

Variables:

- Number of Particles,

- Volume,

## Partition Function[edit]

The partition function, , for a system of identical particles each of mass is given by

where is Planck's constant, is the temperature, is the Boltzmann constant and is the Hamiltonian corresponding to the total energy of the system. For a classical one-component system in a three-dimensional space, , is given by:

where:

- is the de Broglie thermal wavelength (depends on the temperature)

- , with being the Boltzmann constant, and
*T*the temperature.

- 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.