Equipartition and the Virial

A general result that is a direct consequence of ensemble theory is the equipartition theorem, which we state here without proof (for a proof see the book by Huang, in the Further reading section). For a system consisting of particles with coordinates qi,i = 1, 2. 3Ai and momenta Pi,i = 1,2.3N, the equipartition theorem is 

A direct consequence of the equipartition theorem is the following using the hamiltonian equations of motion for such a system 

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