Thermal equilibrium and statistical thermometers in special relativity

Abstract

There is an intense debate in the recent literature about the correct generalization of Maxwell's velocity distribution in special relativity. The most frequently discussed candidate distributions include the Juettner function as well as modifications thereof. Here, we report results from fully relativistic one-dimensional (1D) molecular dynamics (MD) simulations that resolve the ambiguity. The numerical evidence unequivocally favors the Juettner distribution. Moreover, our simulations illustrate that the concept of 'thermal equilibrium' extends naturally to special relativity only if a many-particle system is spatially confined. They make evident that 'temperature' can be statistically defined and measured in an observer frame independent way.