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Consider a classical "degree of freedom" that is linear rather than quadratic: E = c|q| for some constant c

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Consider a classical "degree of freedom" that is linear rather than quadratic: E = c|q| for some constant c. (An example would be the kinetic energy of a highly relativistic particle in one dimension, written in terms of its momentum.) Repeat the derivation of the equipartition theorem for this system, and show that the average energy is kT.