Does classical thermodynamics need a third law? Securing the second law at absolute zero.

This paper elaborates on the formal implications of the relationship between the Second and Third Laws recently established by Martin-Olalla (2025c) and provides a comprehensive formal and historical justification for the logical redundancy of the Nernst heat theorem. By revisiting the Nernst-Einstein debate through the axiomatic frameworks of Planck and Carathéodory, the underlying hypotheses that lead to the traditional view of the Third Law as an independent postulate are examined. It is argued that the historical rejection of Nernst’s proof---motivated by Einstein’s insistence on the practical non-performability of cycles at absolute zero---overlooks the fact that a universal Second Law already precludes such cycles, rendering an independent Third Law an unnecessary complexity. Ultimately, the Nernst theorem is shown to be an essential consistency regulator rather than an independent physical discovery.