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 t