1. The theorem that all Carnot engines operating between two given temperatures have the same efficiency, and no cyclic heat engine operating between two given temperatures is more efficient than a Carnot engine.

2. The theorem that any system has two properties, the thermodynamic temperature T and the entropy S, such that the amount of heat exchanged in an infinitesimal reversible process is given by dQ = TdS; the thermodynamic temperature is a strictly increasing function of the empirical temperature measured on an arbitrary scale.