 Equipartition theorem

Each independent quadratic term in a classical Hamiltonian contributes $k_{B}T/2$ to the mean energy.

The equipartition theorem is a fundamental concept in classical statistical mechanics that states that energy is distributed equally among all degrees of freedom of a system in thermal equilibrium at a given temperature. According to this theorem, each degree of freedom contributes an average energy of \( \frac{1}{2} k_B T \) per degree of freedom to the total energy of the system, where \( k_B \) is the Boltzmann constant and \( T \) is the absolute temperature in Kelvin.