he physical meaning of the law was expressed by Maxwell in the words: "All heat is of the same kind".[2] For this reason, another statement of the law is "All diathermal walls are equivalent".[3]
The law is important for the mathematical formulation of thermodynamics, which needs the assertion that the relation of thermal equilibrium is an equivalence relation. This information is needed for a mathematical definition of temperature that will agree with the physical existence of valid thermometers.[4]