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The excitation temperature () is defined for a population of particles via the Boltzmann factor. It satisfies
where nu and nl represent the number of particles in an upper (e.g. excited) and lower (e.g. ground) state, and gu and gl their statistical weights respectively.
Thus the excitation temperature is the temperature at which we would expect to find a system with this ratio of level populations. However it has no actual physical meaning except when in local thermodynamic equilibrium. The excitation temperature can even be negative for a system with inverted levels (such as a maser).
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