title: Performance of autonomous quantum thermal machines: Hilbert space dimension as a thermodynamical resource.
abstract: Multilevel autonomous quantum thermal machines are discussed. In particular, we explore the relationship 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.
authors.affiliation: Département de Physique Théorique, Université de Genève, 1211 Genève, Switzerland.
authors.forename: Ralph
authors.initials: R
authors.lastname: Silva
authors.affiliation: Departamento de Física Atómica, Molecular y Nuclear and GISC, Universidad Complutense Madrid, 28040 Madrid, Spain.
authors.forename: Gonzalo
authors.initials: G
authors.lastname: Manzano
authors.affiliation: H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom.
authors.forename: Paul
authors.initials: P
authors.lastname: Skrzypczyk
authors.affiliation: Département de Physique Théorique, Université de Genève, 1211 Genève, Switzerland.
authors.forename: Nicolas
authors.initials: N
authors.lastname: Brunner