The Maxwell-Boltzmann velocity distribution in 3D space is f(v)dv=4π(m2πkBT)3/2v2exp(−mv22kBT)dv It gives the probability for a single particle to have a speed in the intervall [v,v+dv]. But this probability is not zero for speeds v>c in conflict with special relativity.
Is there a generalization of the Maxwell-Boltzmann velocity distribution which is valid also in the relativistic regime so that f(v)=0 for v>c ? And how can it be derived? Or can a single particle distribution simply not exist for relativistic speeds, because for high energies, we always have pair-production meaning the particle number is not conserved and a single particle distribution can not be defined in a consistent way?
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