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Local thermodynamic equilibrium (LTE) is a condition, e.g., of a gas, where the variation in temperature is generally small within any specific region, i.e., any temperature gradient is low. For a process significantly involving matter only within a sufficiently short distance, then an assumption of constant temperature, i.e., thermodynamic equilibrium (TE), can serve as a useful approximation. The term is also used for the simplified model implied by this assumption.
The term NLTE (for not or non-LTE or non local thermodynamic equilibrium) is used for an amended LTE-like model that accommodates a common discrepancy from true LTE, specifically, excess electromagnetic radiation invading the locality. Like LTE, it is an approximation used to make stellar models (and other models) tractable. The terms kinetic equilibrium and statistical equilibrium are sometimes used as an alternative to "NLTE" since someone could mistakenly take the term NLTE to mean "global thermodynamic equilibrium" or to mean any other condition that doesn't comply to LTE.