Performance of autonomous quantum thermal machines: Hilbert space dimension as a thermodynamic resource

TL;DR

This paper investigates how increasing the Hilbert space dimension of autonomous quantum thermal machines enhances their performance, showing that larger dimensions enable lower temperatures and higher power, thus establishing dimension as a thermodynamic resource.

Contribution

The study demonstrates that Hilbert space dimension acts as a thermodynamic resource, with larger dimensions improving machine performance and providing insights into the third law of thermodynamics.

Findings

Higher-dimensional machines outperform smaller ones.

Lower temperatures and higher power are achievable with more levels.

Reaching absolute zero requires infinite Hilbert space dimension.

Abstract

Multilevel autonomous quantum thermal machines are discussed. In particular, we explore the relation between the size of the machine (captured by Hilbert space dimension), and the performance of the machine. Using the concepts of virtual qubits and virtual temperatures, we show that higher dimensional machines can outperform smaller ones. For instance, by considering refrigerators with more levels, lower temperatures can be achieved, as well as higher power. We discuss the optimal design for refrigerators of a given dimension. As a consequence we obtain a statement of the third law in terms of Hilbert space dimension: reaching absolute zero temperature requires infinite dimension. These results demonstrate that Hilbert space dimension should be considered a thermodynamic resource.