Equipartition Theorem

The Equipartition Theorem states that in a system at thermal equilibrium, energy is distributed equally among all available degrees of freedom—ways in which particles can store energy, such as motion along axes or rotational movement. Each degree of freedom, on average, holds an amount of energy proportional to the temperature, specifically \(\frac{1}{2}k_B T\), where \(k_B\) is Boltzmann's constant and \(T\) is temperature. This explains why, for example, molecules have predictable amounts of translational and rotational energy at a given temperature, helping us understand the thermal behavior of gases and solids.