Maximum power heat engines and refrigerators in the fast-driving regime

TL;DR

This paper derives the optimal fast-driving cycle, called the generalized Otto cycle, for maximizing power and efficiency in quantum heat engines and refrigerators, applicable to various quantum systems.

Contribution

It introduces a universal optimal cycle for fast-driven thermal machines, extending the Otto cycle with more strokes and providing bounds based on system Hilbert space dimension.

Findings

Optimal cycle maximizes power and cooling in fast-driving regime.

Non-interacting qubits nearly match interacting ones in refrigerator performance.

Many-body effects enhance maximum power and efficiency in heat engines.

Abstract

We study the optimization of the performance of arbitrary periodically driven thermal machines. Within the assumption of fast modulation of the driving parameters, we derive the optimal cycle that universally maximizes the extracted power of heat engines, the cooling power of refrigerators, and in general any linear combination of the heat currents. We denote this optimal solution as ``generalized Otto cycle'' since it shares the basic structure with the standard Otto cycle, but it is characterized by a greater number of fast strokes. We bound this number in terms of the dimension of the Hilbert space of the system used as working fluid. The generality of these results allows for a widespread range of applications, such as reducing the computational complexity for numerical approaches, or obtaining the explicit form of the optimal protocols when the system-baths interactions are characterized by a single thermalization scale. In this case, we compare the thermodynamic performance of a collection of optimally driven non-interacting and interacting qubits. Remarkably, for refrigerators the non-interacting qubits perform almost as well as the interacting ones, while in the heat engine case there is a many-body advantage both in the maximum power, and in the efficiency at maximum power. Additionally, we illustrate our general results studying the paradigmatic model of a qutrit-based heat engine. Our results strictly hold in the semiclassical case in which no coherence is generated by the driving, and finally we discuss the non-commuting case.