The maximum efficiency of nano heat engines depends on more than temperature

TL;DR

This paper revises Carnot's theorem for quantum nanoregime heat engines, showing efficiency depends on bath structure and quantum constraints, not just temperature, impacting nanoscale thermal machine design.

Contribution

It introduces a modified maximum efficiency formula for quantum heat engines with finite baths, incorporating quantum information measures like max relative entropy.

Findings

Maximum efficiency can be less than Carnot when bath structure is unfavorable.

Efficiency is governed by second law or max relative entropy in the quantum regime.

Bath Hamiltonian choices influence the achievable efficiency of quantum heat engines.

Abstract

Sadi Carnot's theorem regarding the maximum efficiency of heat engines is considered to be of fundamental importance in thermodynamics. This theorem famously states that the maximum efficiency depends only on the temperature of the heat baths used by the engine, but not on the specific structure of baths. Here, we show that when the heat baths are finite in size, and when the engine operates in the quantum nanoregime, a revision to this statement is required. We show that one may still achieve the Carnot efficiency, when certain conditions on the bath structure are satisfied; however if that is not the case, then the maximum achievable efficiency can reduce to a value which is strictly less than Carnot. We derive the maximum efficiency for the case when one of the baths is composed of qubits. Furthermore, we show that the maximum efficiency is determined by either the standard second law of thermodynamics, analogously to the macroscopic case, or by the non increase of the max relative entropy, which is a quantity previously associated with the single shot regime in many quantum protocols. This relative entropic quantity emerges as a consequence of additional constraints, called generalized free energies, that govern thermodynamical transitions in the nanoregime. Our findings imply that in order to maximize efficiency, further considerations in choosing bath Hamiltonians should be made, when explicitly constructing quantum heat engines in the future. This understanding of thermodynamics has implications for nanoscale engineering aiming to construct small thermal machines.