The equipartition theorem states that energy is distributed equally among all degrees of freedom of a system in thermal equilibrium. This principle connects to how particles behave statistically, indicating that each degree of freedom contributes an average energy of $$\frac{1}{2} kT$$, where $k$ is the Boltzmann constant and $T$ is the temperature in Kelvin. It plays a critical role in understanding the behavior of particles in various statistical ensembles and helps explain the distribution of energy in systems at thermal equilibrium.
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