Consider a classical of freedom" that is linear rather than quadratic: E = clql 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 E= kT.

Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter14: Special Theory Of Relativity
Section: Chapter Questions
Problem 14.40P
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Consider a classical of freedom" that is linear rather than quadratic: E = clql 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 E= kT. 

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