Canonical ensemble

Canonical Ensemble:

Variables:

• Number of Particles, $N$

• Volume, $V$

• Temperature, $T$

Partition Function

Classical Partition Function (one-component system) in a three-dimensional space: $Q_{NVT}$

$Q_{NVT}={\frac {V^{N}}{N!\Lambda ^{3N}}}\int d(R^{*})^{3N}\exp \left[-\beta U\left(V,(R^{*})^{3N}\right)\right]$

where:

• $\Lambda$ is the de Broglie wavelength

• $\beta ={\frac {1}{k_{B}T}}$, with $k_{B}$ being the Boltzmann's constant

• $U$ is the potential energy, which depends on the coordinates of the particles (and on the interaction model)