Virtual qubits, virtual temperatures, and the foundations of thermodynamics

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 analyzing 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.

Minimal Self-Contained Quantum Refrigeration Machine Based on Four Quantum Dots

“…The average occupations of the virtual qubit levels (determined by the coupling with the reservoirs H, R 1 and R 2 ) defines the effective (average) temperature of H, R 1 and R 2 which is perceived by QD 2 : such temperature competes with T C in cooling down the dot and can be identified with the value of T * C of our model. Observing that the energy levels of |0, 0, 0, 1 and |d are ǫ 4 , ǫ 1 + ǫ 3 + U d respectively, from [6] we get…”

“…Interestingly for T H /T R → ∞ the value of T * C appears to asymptotically converge toward a finite non-zero temperature which depends upon the engine microscopic parameters and which can be interpreted as the emergent absolute zero of the model. An approximate analytical expression for T * C can be derived exploiting the recent general theory of genuine, maximally-efficient self-contained quantum thermal machines [6]. This is done by interpreting the quadridot as a composite system, consisting of an "effective" virtual qubit formed by the states |0, 0, 0, 1 and |d which (through g dd ) mediates the interaction between QD 2 and the reservoirs H, R 1 and R 2 .…”

“…The progress in this field may as well have important applications in the control of heat transport in nano-devices [3]. In a series of recent works [4][5][6] the fundamental limits to the dimensions of a quantum refrigerator have been found. It has been further demonstrated that these machines could still attain Carnot-efficiency [5] thus launching the call for the implementation of the smallest possible quantum refrigerator.…”

“…Refs. [4][5][6] considered selfcontained thermal machines defined as those that perform a cycle without the supply of external work, their action being grounded on the steady-state heat transfer from thermal reservoirs at different temperatures. The major difficulty in the realization [7,8] of self-contained refrigerators (SCRs) is the engineering of the crucial three-body interaction enabling the coherent transition between a doubly excited state in contact with a hot (H) and cold (C) reservoir, and a singly-excited state coupled to an intermediate (or "room" -R) temperature bath.…”

Deep-subwavelength lithography via graphene plasmons

“…This development has benefited in particular from emerging experimental technologies in AMO and NEMS systems, as evidenced in particular by the single ion heat engine theoretically proposed [1] and experimentally demonstrated [2]. Additional approaches being considered involve spin systems [3,4], qubit systems [5], ultracold atoms [6], cavity-assisted atom-light systems [7], nanomechanical resonators [8], and optomechanical systems [9][10][11][12][13][14].…”