Autonomous Quantum Devices: When Are They Realizable without Additional Thermodynamic Costs?

Abstract

The resource theory of quantum thermodynamics has been a very successful theory and has generated much follow-up work in the community. It requires energy-preserving unitary operations to be implemented over a system, bath, and catalyst as part of its paradigm. So far, such unitary operations have been considered a “free” resource in the theory. However, this is only an idealization of a necessarily inexact process. Here, we include an additional auxiliary control system which can autonomously implement the unitary by turning an interaction “on or off.” However, the control system will inevitably be degraded by the backaction caused by the implementation of the unitary. We derive conditions on the quality of the control device so that the laws of thermodynamics do not change and prove—by utilizing a good quantum clock—that the laws of quantum mechanics allow the backreaction to be small enough so that these conditions are satisfiable. Our inclusion of nonidealized control into the resource framework also raises interesting prospects, which were absent when considering idealized control. Among other things, the emergence of a third law without the need for the assumption of a light cone. Our results and framework unify the field of autonomous thermal machines with the thermodynamic quantum resource-theoretic one, and lay the groundwork for all quantum processing devices to be unified with fully autonomous machines.

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Plain Language Summary

The second law of thermodynamics provides a constraint on whether a transition between two states of a system is possible. The necessary control and costs for such transitions are well understood. In the last decade or so, scientists have studied thermodynamics in the quantum regime, giving rise to new quantum-mechanical thermodynamic laws. However, this new regime for thermodynamics requires a far greater level of precision and control for transitions to occur. Here, we explore the often-asked question of whether there are unaccounted-for thermodynamic costs required in the implementation of this control. We find that the new laws do not require revision since the costs of control can be made arbitrarily small.

We start by mathematically describing an external agent that performs energy-preserving operations on a system and then introduce a clock that turns on and off the interactions implementing these operations. We then derive conditions so that the change in the clock’s state due to the backreaction on it has a vanishingly small thermodynamic cost and show that clocks exist that satisfy this criterion.

Our results come with fine print: The control cannot be implemented too quickly. This requirement, while ever present at the macroscopic scale, was missing in the quantum-mechanical version of the law. So, in a strange twist of fate, our results show that this constraining property was lurking out of sight all along in the control.

We studied just a single control event—the interaction was switched on and then switched off. However, in a quantum engine, the microscopic working body is periodically coupled to cold and hot reservoirs. Future work might analyze such multiple-control events.