What theorem is the historical basis of the third law of thermodynamics?

The Nernst heat theorem is the historical basis of the third law of thermodynamics.

Walther Nernst formulated the theorem while studying chemical reactions and the behavior of matter at very low temperatures. Developed mainly between 1906 and 1912, it stated that the entropy changes associated with isothermal processes tend toward zero as the temperature approaches absolute zero. This helped establish the modern third law.

The third law is commonly expressed by saying that a perfect crystal has zero entropy at absolute zero, 0 K. More generally, the entropy at absolute zero is fixed by the degeneracy of the ground state. A crystal with more than one equally available ground-state arrangement can therefore retain residual entropy.

The theorem is also called the Nernst–Simon theorem, recognizing Francis Simon’s later contributions. That name does not make “Nernst heat theorem” wrong: it is the standard historical label and the usual answer in a general thermodynamics quiz. The third law also explains why absolute zero cannot be reached through a finite sequence of thermodynamic operations.