Zeroth Law of Thermodynamics

The Zeroth law of thermodynamics states:

If a system $A$ is in thermal equilibrium with a system $C$, and a system $B$ is also, separately, in thermal equilibrium with the same system $C$, then $A$ and $B$ are necessarily in thermal equilibrium with each other as well -- even without ever being placed in direct contact.

This statement may sound almost too obvious to need stating, but it carries real physical content: it says that "being in thermal equilibrium with" is a transitive relation, in exactly the same sense that "being equal in value to" is transitive for numbers. It is entirely conceivable, logically, for a relation to fail to be transitive (many everyday relations, such as "is a friend of," are not transitive), so the Zeroth law is a genuine physical statement about how heat and temperature behave, not a matter of pure logic.

The law is called the "Zeroth" law because it was recognised as a necessary, independent postulate of thermodynamics only after the first and second laws had already been formulated and named; being logically more fundamental than both (in fact required for the very definition of temperature that the other laws use), it was inserted "before" them in the numbering, as the zeroth law. …