Characterizing the Carnot cycle at absolute zero: a reply to "Comment on 'Proof of the Nernst theorem' "

This reply addresses a recent comment concerning the proof of the Nernst theorem. I clarify how a Carnot engine can consistently operate at $T=0$ through a continuous deformation of a cycle operating at $T>0$. By examining the limit where heat exchange with the cold reservoir vanishes, I show that the Nernst theorem ensures that the concept of temperature remains physically consistent at the absolute zero limit. SuppMaterial is a pdf animation showing the characterization of T=0 through a limit Carnot engine. The animation requires a pdf viewer with javascript enabled.