Empirical temperature ($\theta$)

An empirical temperature labels classes of thermal equilibrium using a reproducible thermometer response. Equal labels express the zeroth law of thermodynamics comparison. A suitable continuous response and calibration let ordinary laboratory states be represented on a numerical scale; the abstract equivalence relation alone does not guarantee a useful real-valued coordinate. An injective function of the label preserves equality, so the zeroth law of thermodynamics alone fixes neither unit nor spacing. Thermometer calibration supplies a chosen response relation; thermodynamic temperature supplies the additional absolute-scale structure.