Virtual qubits, virtual temperatures, and the foundations of thermodynamics

TLDR

Virtual qubits are two‑level subsystems of a composite heat‑bath system, and their virtual temperatures can assume any value, positive or negative. The authors argue that thermal machines can be understood via virtual qubits at virtual temperatures, viewing the two heat baths as a composite system, and introduce the concepts of genuine thermal machines and the strength of work. They demonstrate that thermal machines operate by coupling an external system to selected virtual qubits and temperatures, as shown through analysis of the smallest thermal machines. This virtual‑qubit framework explains phenomena such as approaching Carnot efficiency through equivalence to the smallest machines, entropy production in irreversible machines, and interpreting work via negative temperature and population inversion, while also defining genuine thermal machines and the notion of work strength.

Abstract

We argue that thermal machines can be understood from the perspective of `virtual qubits' at `virtual temperatures': The relevant way to view the two heat baths which drive a thermal machine is as a composite system. Virtual qubits are two-level subsystems of this composite, and their virtual temperatures can take on any value, positive or negative. Thermal machines act upon an external system by placing it in thermal contact with a well-selected range of virtual qubits and temperatures. We demonstrate these claims by studying the smallest thermal machines. We show further that this perspective provides a powerful way to view thermodynamics, by analysing a number of phenomena. This includes approaching Carnot efficiency (where we find that all machines do so essentially by becoming equivalent to the smallest thermal machines), entropy production in irreversible machines, and a way to view work in terms of negative temperature and population inversion. Moreover we introduce the idea of "genuine" thermal machines and are led to considering the concept of "strength" of work.