We develop the analogue of the law of equipartition of energy for relativistic systems and examine some of its consequences. For mixtures of special relativistic ideal gases of different rest masses we find that the energy gets partitioned in an unexpected way, the ultra-relativistic component taking essentially twice as much energy per degree of freedom as the more massive non-relativistic component. This conclusion may have an application when considering thermalized photons in the interior of the sun. With an eye toward the possible extension of our considerations to general relativity, we show that, in the presence of a distinguished time-like Killing field, the global parameter which characterized the equilibrium state of an ideal gas can be determined by local measurements employing a suitably calibrated thermometer.
KeywordsGeneral Relativity Equilibrium State Differential Geometry Local Measurement Relativistic System
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