Carnot Cycle at Finite Power: Attainability of Maximal Efficiency

TL;DR

This paper investigates the possibility of reaching Carnot efficiency at finite power, revealing that realistic interactions lead to long cycle times and low power, but engineered interactions can achieve high efficiency with finite power.

Contribution

It generalizes the Carnot cycle to non-slow processes and links engine efficiency to computational complexity and protein folding paradoxes, proposing engineered interactions for finite power high efficiency.

Findings

Realistic engine-bath interactions result in long cycle times and low power near maximal efficiency.

Engineers can design interactions to achieve high efficiency at finite power.

The study connects thermodynamics with computational complexity and biological folding problems.

Abstract

We want to understand whether and to which extent the maximal (Carnot) efficiency for heat engines can be reached at a finite power. To this end we generalize the Carnot cycle so that it is not restricted to slow processes. We show that for realistic (i.e. not purposefully-designed) engine-bath interactions, the work-optimal engine performing the generalized cycle close to the maximal efficiency has a long cycle time and hence vanishing power. This aspect is shown to relate to the theory of computational complexity. A physical manifestation of the same effect is the Levinthal's paradox in the protein folding problem. The resolution of this paradox for realistic proteins allows to construct engines that can extract at a finite power 40% of the maximally possible work reaching 90% of the maximal efficiency. For purposefully designed engine-bath interactions, the Carnot efficiency is achievable at a large power.