In Special Relativity
For a single particle in special relativity, it is not the case that . Instead, it is true that and
The last expression can be simplified to either or .
Thus, under the conditions described in earlier sections (including Newton's third law of motion, despite relativity), the time average for particles with a power law potential is
In particular, the ratio of kinetic energy to potential energy is no longer fixed, but necessarily falls into an interval:
where the more relativistic systems exhibit the larger ratios.
Read more about this topic: Virial Theorem
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