Equipartition
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Equipartition usually refers to the fact that
- in classical statistical mechanics each degree of freedom that appears quadratically in the energy (Hamiltonian) has an average value of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}k_B T} , where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3}{2}k_B T} , since translations are described by three degrees of freedom.
For elastic waves, equipartition refers to the fact that the average potential and kinetic energies are equal (and therefore equal to half the total energy, which is thereby "equipartitioned".)