Is Maxwell's Distribution Law Applicable to High Speed Particles?

[astro2cosmos]

does maxwell distribution law of velocity of gas also applicable for very high speed near to speed of light? means can we apply this law to particles like proton, positron?

 

[phyzguy]

No, it assumes E = p^2/2m. But this is true even for electrons and protons as long as the temperature is reasonable. Even at the center of the sun the velocity of the electrons and protons is non-relativistic. You need to reach billions of degrees K before relativistic corrections come into play. At these temperatures the Maxwell distribution needs to be modified.