The zeroth law of thermodynamics states that if two thermodynamic systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. Accordingly, thermal equilibrium between systems is a transitive relation.
Two systems are said to be in thermal equilibrium with respect to each other if they are linked by a wall permeable only to heat and they do not change over time. As a convenience of language, the same is also sometimes said of unlinked systems that would not change if they did have such a wall.
The physical meaning is expressed by Maxwell in the statement: "All heat is of the same kind". Another statement of the law is "All diathermal walls are equivalent".The law is important for the mathematical formulation of thermodynamics, which depends on the assertion that the relation of thermal equilibrium is an equivalence relation, The condition justifies the use of practical thermometers.