1School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland
2Centre for complex quantum systems, Aarhus University, Nordre Ringgade 1, 8000 Aarhus C, Denmark
3Dahlem Center for Complex Quantum Systems, Freie Universit at Berlin, 14195 Berlin, Germany
4School of Physics, University College Dublin, Belfield, Dublin 4, Ireland
5Centre for Quantum Engineering, Science, and Technology, University College Dublin, Belfield, Dublin 4, Ireland
6Departamento de Física, Universidad de Murcia, Murcia E-30071, Spain
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Abstract
We introduce unique class of cyclic quantum thermal machines (QTMs) which can maximize their performance at the finite value of cycle duration $tau$ where they are most irreversible. These QTMs are based on single-stroke thermodynamic cycles realized by the non-equilibrium steady state (NESS) of the so-called Periodically Refreshed Baths (PReB) process. We find that such QTMs can interpolate between standard collisional QTMs, which consider repeated interactions with single-site environments, and autonomous QTMs operated by simultaneous coupling to multiple macroscopic baths. We discuss the physical realization of such processes and show that their implementation requires a finite number of copies of the baths. Interestingly, maximizing performance by operating in the most irreversible point as a function of $tau$ comes at the cost of increasing the complexity of realizing such a regime, the latter quantified by the increase in the number of copies of baths required. We demonstrate this physics considering a simple example. We also introduce an elegant description of the PReB process for Gaussian systems in terms of a discrete-time Lyapunov equation. Further, our analysis also reveals interesting connections with Zeno and anti-Zeno effects.
Featured image: A simple periodically refreshed quantum thermal machine. It consists of two fermionic sites with hopping $g$ between them, each site having its own set of baths, which couple one-by-one for a time $tau$ in a cyclic fashion. Here each bath is described by a single dissipative fermionic site. The dissipation 'refreshes' each bath to its equilibrium state before it is re-coupled to the system. The temperatures of the equilibrium states of the set of baths attached to the two sites are different (inverse temperatures, $beta_1$ and $beta_2$), while the chemical potentials ($mu$) are same.
Popular summary
Based on microscopic quantum systems, we propose a new type of thermodynamic cycle that can be most efficient when dissipation is maximized as a function of cycle duration. Consequently, as a function of cycle duration, there is no trade-off between power and efficiency. We call heat engines and refrigerators based on this thermodynamic cycle "periodically refreshed quantum thermal machines." Unlike traditional thermal machines, the system does not return to an equilibrium state at the end of each cycle, but rather to a far-from-equilibrium state. We discuss how such a process could be physically realized. The nature of the cycle makes the system's dynamics and thermodynamics amenable to exact numerical treatment within existing microscopic approaches to quantum thermodynamics. In particular, for Gaussian systems, we find an elegant description in terms of a discrete-time Lyapunov equation: a well-studied equation in mathematics and engineering that is used in everyday life for control of macroscopic objects. "Periodically refreshed quantum thermal machines" combine several concepts, demonstrating deep connections with the physics of repeated interaction or collisional models, thermoelectric devices, and quantum Zeno and anti-Zeno effects.
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