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The kinetic theory offers a valuable but limited account of the behavior of the materials of macroscopic systems. It indicates the absolute temperature as proportional to the average kinetic energy of the random microscopic motions of their constituent microscopic particles such as electrons, atoms, and molecules."
Temperature - Wikipedia, the free encyclopedia
your wiki quote is fully in accordance to what I said. macroscopic systems! it is the average kinetic energy of many, many particles that defines temperature.
The quote is discussing macroscopic systems. It says the temperature of a macrosocopic system - a body - is proportional to the average kinetic energy of its constituent particles. It sets no lower limit on the number of constituent particles. If you want me to believe your contention, show me such a limitation.
a particle with [x] energy can come from just about any background cohort. likewise, a blackbody photon [y] can come from just about any temperature material (the limitiations are on high end radiation not low end). one single particle cannot collide with itself nor be its own reference frame therefore you cannot assign it a 'temperature'.
You yourself just admitted that a lone particle may have [x] energy. Collisions are NOT mentioned in the definition of temperature; neither are the loss or gain of photons, the existence of background cohorts nor any sort of reference frame. Transmission is not required to hold the characteristic. All matter has some level of kinetic energy and thus a temperature. "All matter" includes individual particles.