Equipartition Theorem

WIP
Essentially states that the thermal energy of a particle is split equally between different kinetic energies such as the three translational energies, rotational energies, and vibrational energies

$K=\frac{3}{2}{k}_{B}T$

• $K$ is the kinetic energy of the particle
• $k_B$ is the Boltzmann Constant
• $T$ is temperature

$⟨{\epsilon }_j⟩=\frac{\tau }{n}$

$⟨U_{\text{ideal gas}}⟩=\frac{3}{2}N\tau$

$⟨U_{\text{1D HO}}⟩=\tau$

$⟨U_{\text{3D HO}}⟩=3\tau$