We formulate reheating as a constrained variational problem in the space of equation-of-state histories, rather than attempting to describe it through microscopic models. We introduce a regularized functional framework that identifies reheating histories which extremize a given cosmological observable under minimal physical assumptions. As illustrative applications, we consider prompt gravitational waves, induced gravitational waves, and primordial black holes. We find that different observables select qualitatively different regions of reheating-history space. These examples demonstrate that cosmological observables define distinct extremal directions in reheating-history space and can therefore be used to systematically explore the space of post-inflationary expansion histories.

This paper elaborates on the implications of the relationship between the Second and Third Laws and provides a comprehensive formal and historical justification for the logical redundancy of the Nernst heat theorem. By revisiting the Nernst-Einstein debate, 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.