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We show that Kompaneetz equation describing photon diffusion in anenvironment of an electron gas, when linearized around its equilibriumdistribution, coincides with the relativistic diffusion discussed in recentpublications. The model of the relativistic diffusion is related to solublemodels of imaginary time quantum mechanics. We suggest some non-lineargeneralizations of the relativistic diffusion equation and their astrophysicalapplications (in particular to the Sunyaev-Zeldovich effect).

Linearized Kompaneetz equation as a relativistic diffusion