The excited-state population distribution in hydrogen plasma can define various excitation temperatures. The relationship between "various temperatures" was examined in a macroscopic sense, and "statistical mechanical temperature" is derived from partial differential calculations using entropy. As a result, by approximating the excited-state number density as a q-exponential distribution, it was found that the temperature calculated from the partial derivative of the q-average energy with respect to Tsallis entropy, that by the q-average energy alone, and that calculated as the Lagrange multiplier from the coefficient in the argument of the q-distribution all match. The possibility of uniquely defining temperature is found even in non-equilibrium by appropriately defining statistical mechanics and non-additive entropy.
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