Zeroth Law of Thermodynamics

The zeroth law of thermodynamics -- also called the law of thermal equilibrium -- is a curious historical case: it was formulated and named only AFTER the first and second laws already existed, yet logically it has to come first, because it is what makes the very concept of "temperature" rigorous in the first place. Placing it "before" the other two, and numbering it zero rather than fourth, reflects that logical priority rather than the order of discovery.

The law itself states: if two systems are separately in thermal equilibrium with a third system, then they are also in thermal equilibrium with each other. Concretely, if system B is in thermal equilibrium with system A, and system C is also (separately) in thermal equilibrium with the same system A, then B and C must be in thermal equilibrium with one another too -- even without B and C ever having been placed in direct contact. …