# Equipartition

in classical statistical mechanics each degree of freedom that appears quadratically in the energy (Hamiltonian) has an average value of $\frac{1}{2}k_B T$, where $k_B T$ is the thermal energy.
Thus, the thermal energy is shared equally ("equipartitioned") by all these degrees of freedom. This is a consequence of the equipartition theorem, which is very simple mathematically. As an immediate corollary, the translational energy of a molecule must equal $\frac{3}{2}k_B T$, since translations are described by three degrees of freedom.