Juttner Distribution From Photon Absorption and the Maxwell-Boltzmann Factor

  In (1), the Juttner distribution for a particle is obtained by considering reaction balance using photon absorption and emission by a particle. It is stated in (1) that the Maxwell-Boltzmann factor exp(-E/T) is not explicitly used. The photon is associated with blackbody radiation and the Bose-Einstein form for <nk> is used. We argue that the Bose-Einstein form is linked to a reaction balance form with:  P(ei) / {1+P(ei)} = exp(-ei/T), where ei is photon energy. This exact ratio appears in a particle-photon balance equation in (1) ensuring that p(particle e2) = p(particle e1) exp(- (e2-e1)/T) or that p(particle e) = C exp(-e/T). In other words, the implicit assumption in the photon absorption-emission equilibrium problem is: p(particle e1)p(particle e2) = p(particle e1+e2) which is equivalent to the Maxwell-Boltzmann factor.