Efficiency bounds for nonequilibrium heat engines

TL;DR

This paper establishes fundamental efficiency bounds for heat engines operating with a single reservoir, revealing that ergodic engines cannot reach Carnot efficiency, while non-ergodic engines can surpass it, based on nonequilibrium thermodynamics.

Contribution

The paper derives rigorous thermodynamic bounds for both ergodic and non-ergodic engines using relative entropy, extending classical limits to nonequilibrium processes.

Findings

Ergodic engines are limited below Carnot efficiency.

Non-ergodic engines can exceed the Carnot bound.

Efficiency bounds are given by relative entropy between distributions.

Abstract

We analyze the efficiency of thermal engines (either quantum or classical) working with a single heat reservoir like atmosphere. The engine first gets an energy intake, which can be done in arbitrary non-equilibrium way e.g. combustion of fuel. Then the engine performs the work and returns to the initial state. We distinguish two general classes of engines where the working body first equilibrates within itself and then performs the work (ergodic engine) or when it performs the work before equilibrating (non-ergodic engine). We show that in both cases the second law of thermodynamics limits their efficiency. For ergodic engines we find a rigorous upper bound for the efficiency, which is strictly smaller than the equivalent Carnot efficiency. I.e. the Carnot efficiency can be never achieved in single reservoir heat engines. For non-ergodic engines the efficiency can be higher and can exceed the equilibrium Carnot bound. By extending the fundamental thermodynamic relation to nonequilibrium processes, we find a rigorous thermodynamic bound for the efficiency of both ergodic and non-ergodic engines and show that it is given by the relative entropy of the non-equilibrium and initial equilibrium distributions.These results suggest a new general strategy for designing more efficient engines. We illustrate our ideas by using simple examples.