This work presents a novel derivation of the expressions that describe the distortions of the cosmic microwave background curve due to the interactions between photons and the electrons present in dilute ionized systems. In this approach, a simplified one-dimensional evolution equation for the photon number occupation is applied to describe the mentioned interaction. This methodology emphasizes the physical features of the Sunyaev-Zeldovich effect and suggests the existence of links between basic statistical physics and complex applications involving radiative processes.
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